How to find f(x) - SAT Math
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Let f(x, y) = x2y2 – xy + y. If a = f(1, 3), and b = f(–2, –1), then what is f(a, b)?
Let f(x, y) = x2y2 – xy + y. If a = f(1, 3), and b = f(–2, –1), then what is f(a, b)?
f(x, y) is defined as x2y2 – xy + y. In order to find f(a, b), we will need to first find a and then b.
We are told that a = f(1, 3). We can use the definition of f(x, y) to determine the value of a.
a = f(1, 3) = 1232 – 1(3) + 3 = 1(9) – 3 + 3 = 9 + 0 = 9
a = 9
Similarly, we can find b by determining the value of f(–2, –1).
b = f(–2, –1) = (–2)2(–1)2 – (–2)(–1) + –1 = 4(1) – (2) – 1 = 4 – 2 – 1 = 1
b = 1
Now, we can find f(a, b), which is equal to f(9, 1).
f(a, b) = f(9, 1) = 92(12) – 9(1) + 1 = 81 – 9 + 1 = 73
f(a, b) = 73
The answer is 73.
f(x, y) is defined as x2y2 – xy + y. In order to find f(a, b), we will need to first find a and then b.
We are told that a = f(1, 3). We can use the definition of f(x, y) to determine the value of a.
a = f(1, 3) = 1232 – 1(3) + 3 = 1(9) – 3 + 3 = 9 + 0 = 9
a = 9
Similarly, we can find b by determining the value of f(–2, –1).
b = f(–2, –1) = (–2)2(–1)2 – (–2)(–1) + –1 = 4(1) – (2) – 1 = 4 – 2 – 1 = 1
b = 1
Now, we can find f(a, b), which is equal to f(9, 1).
f(a, b) = f(9, 1) = 92(12) – 9(1) + 1 = 81 – 9 + 1 = 73
f(a, b) = 73
The answer is 73.
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Let F(x) = _x_3 + 2_x_2 – 3 and G(x) = x + 5. Find F(G(x))
Let F(x) = _x_3 + 2_x_2 – 3 and G(x) = x + 5. Find F(G(x))
F(G(x)) is a composite function where the expression G(x) is substituted in for x in F(x)
F(G(x)) = (x + 5)3 + 2(x + 5)2 – 3 = x_3 + 17_x_2 + 95_x + 172
G(F(x)) = _x_3 + _x_2 + 2
F(x) – G(x) = _x_3 + 2_x_2 – x – 8
F(x) + G(x) = _x_3 + 2_x_2 + x + 2
F(G(x)) is a composite function where the expression G(x) is substituted in for x in F(x)
F(G(x)) = (x + 5)3 + 2(x + 5)2 – 3 = x_3 + 17_x_2 + 95_x + 172
G(F(x)) = _x_3 + _x_2 + 2
F(x) – G(x) = _x_3 + 2_x_2 – x – 8
F(x) + G(x) = _x_3 + 2_x_2 + x + 2
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What is the value of xy_2(xy – 3_xy) given that x = –3 and y = 7?
What is the value of xy_2(xy – 3_xy) given that x = –3 and y = 7?
Evaluating yields –6174.
–147(–21 + 63) =
–147 * 42 = –6174
Evaluating yields –6174.
–147(–21 + 63) =
–147 * 42 = –6174
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If z + 2x = 10 and 7z + 2x = 16, what is z?
If z + 2x = 10 and 7z + 2x = 16, what is z?
Subtract the first expression from the second. That gives you 6z = 6. That simplifies to z = 1.
Subtract the first expression from the second. That gives you 6z = 6. That simplifies to z = 1.
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If the function g is defined by g(x) = 4_x_ + 5, then 2_g_(x) – 3 =
If the function g is defined by g(x) = 4_x_ + 5, then 2_g_(x) – 3 =
The function g(x) is equal to 4_x_ + 5, and the notation 2_g_(x) asks us to multiply the entire function by 2. 2(4_x_ + 5) = 8_x_ + 10. We then subtract 3, the second part of the new equation, to get 8_x_ + 7.
The function g(x) is equal to 4_x_ + 5, and the notation 2_g_(x) asks us to multiply the entire function by 2. 2(4_x_ + 5) = 8_x_ + 10. We then subtract 3, the second part of the new equation, to get 8_x_ + 7.
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If f(x) = x_2 + 5_x and g(x) = 2, what is f(g(4))?
If f(x) = x_2 + 5_x and g(x) = 2, what is f(g(4))?
First you must find what g(4) is. The definition of g(x) tells you that the function is always equal to 2, regardless of what “x” is. Plugging 2 into f(x), we get 22 + 5(2) = 14.
First you must find what g(4) is. The definition of g(x) tells you that the function is always equal to 2, regardless of what “x” is. Plugging 2 into f(x), we get 22 + 5(2) = 14.
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f(a) = 1/3(a_3 + 5_a – 15)
Find a = 3.
f(a) = 1/3(a_3 + 5_a – 15)
Find a = 3.
Substitute 3 for all a.
(1/3) * (33 + 5(3) – 15)
(1/3) * (27 + 15 – 15)
(1/3) * (27) = 9
Substitute 3 for all a.
(1/3) * (33 + 5(3) – 15)
(1/3) * (27 + 15 – 15)
(1/3) * (27) = 9
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Evaluate f(g(6)) given that f(x) = _x_2 – 6 and g(x) = –(1/2)x – 5
Evaluate f(g(6)) given that f(x) = _x_2 – 6 and g(x) = –(1/2)x – 5
Begin by solving g(6) first.
g(6) = –(1/2)(6) – 5
g(6) = –3 – 5
g(6) = –8
We substitute f(–8)
f(–8) = (–8)2 – 6
f(–8) = 64 – 6
f(–8) = 58
Begin by solving g(6) first.
g(6) = –(1/2)(6) – 5
g(6) = –3 – 5
g(6) = –8
We substitute f(–8)
f(–8) = (–8)2 – 6
f(–8) = 64 – 6
f(–8) = 58
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If f(x) = |(_x_2 – 175)|, what is the value of f(–10) ?
If f(x) = |(_x_2 – 175)|, what is the value of f(–10) ?
If x = –10, then (_x_2 – 175) = 100 – 175 = –75. But the sign |x| means the absolute value of x. Absolute values are always positive.
|–75| = 75
If x = –10, then (_x_2 – 175) = 100 – 175 = –75. But the sign |x| means the absolute value of x. Absolute values are always positive.
|–75| = 75
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If f(x)= 2x² + 5x – 3, then what is f(–2)?
If f(x)= 2x² + 5x – 3, then what is f(–2)?
By plugging in –2 for x and evaluating, the answer becomes 8 – 10 – 3 = -5.
By plugging in –2 for x and evaluating, the answer becomes 8 – 10 – 3 = -5.
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If f(x) = x² – 2 and g(x) = 3x + 5, what is f(g(x))?
If f(x) = x² – 2 and g(x) = 3x + 5, what is f(g(x))?
To find f(g(x) plug the equation for g(x) into equation f(x) in place of “x” so that you have: f(g(x)) = (3x + 5)² – 2.
Simplify: (3x + 5)(3x + 5) – 2
Use FOIL: 9x² + 30x + 25 – 2 = 9x² + 30x + 23
To find f(g(x) plug the equation for g(x) into equation f(x) in place of “x” so that you have: f(g(x)) = (3x + 5)² – 2.
Simplify: (3x + 5)(3x + 5) – 2
Use FOIL: 9x² + 30x + 25 – 2 = 9x² + 30x + 23
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If f(x)=3x and g(x)=2x+2, what is the value of f(g(x)) when x=3?
If f(x)=3x and g(x)=2x+2, what is the value of f(g(x)) when x=3?
With composition of functions (as with the order of operations) we perform what is inside of the parentheses first. So, g(3)=2(3)+2=8 and then f(8)=24.
With composition of functions (as with the order of operations) we perform what is inside of the parentheses first. So, g(3)=2(3)+2=8 and then f(8)=24.
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The cost of a cell phone plan is $40 for the first 100 minutes of calls, and then 5 cents for each minute after. If the variable x is equal to the number of minutes used for calls in a month on that cell phone plan, what is the equation f(x) for the cost, in dollars, of the cell phone plan for calls during that month?
The cost of a cell phone plan is $40 for the first 100 minutes of calls, and then 5 cents for each minute after. If the variable x is equal to the number of minutes used for calls in a month on that cell phone plan, what is the equation f(x) for the cost, in dollars, of the cell phone plan for calls during that month?
40 dollars is the constant cost of the cell phone plan, regardless of minute usage for calls. We then add 5 cents, or 0.05 dollars, for every minute of calls over 100. Thus, we do not multiply 0.05 by x, but rather by (x - 100), since the 5 cent charge only applies to minutes used that are over the 100-minute barrier. For example, if you used 101 minutes for calls during the month, you would only pay the 5 cents for that 101st minute, making your cost for calls $40.05. Thus, the answer is 40 + 0.05(x - 100).
40 dollars is the constant cost of the cell phone plan, regardless of minute usage for calls. We then add 5 cents, or 0.05 dollars, for every minute of calls over 100. Thus, we do not multiply 0.05 by x, but rather by (x - 100), since the 5 cent charge only applies to minutes used that are over the 100-minute barrier. For example, if you used 101 minutes for calls during the month, you would only pay the 5 cents for that 101st minute, making your cost for calls $40.05. Thus, the answer is 40 + 0.05(x - 100).
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f(x) = 4x + 2
g(x) = 3x - 1
The two equations above define the functions f(x) = g(x). If f(d) = 2g(d) for some value of d, then what is the value of d?
f(x) = 4x + 2
g(x) = 3x - 1
The two equations above define the functions f(x) = g(x). If f(d) = 2g(d) for some value of d, then what is the value of d?
f(x) = 4x + 2
g(x) = 3x - 1
We have f(d) = 2g(d). We multiply each value in g(d) by 2.
4d + 2 = 2(3d - 1) (Distribute the 2 in the parentheses by multiplying each value in them by 2.)
4d + 2 = 6d - 2 (Add 2 to both sides.)
4d + 4 = 6d (Subtract 4d from both sides.)
4 = 2d (Divide both sides by 2.)
2 = d
We can plug that back in to double check.
4(2) + 2 = 6(2) - 2
8 + 2 = 12 - 2
10 = 10
f(x) = 4x + 2
g(x) = 3x - 1
We have f(d) = 2g(d). We multiply each value in g(d) by 2.
4d + 2 = 2(3d - 1) (Distribute the 2 in the parentheses by multiplying each value in them by 2.)
4d + 2 = 6d - 2 (Add 2 to both sides.)
4d + 4 = 6d (Subtract 4d from both sides.)
4 = 2d (Divide both sides by 2.)
2 = d
We can plug that back in to double check.
4(2) + 2 = 6(2) - 2
8 + 2 = 12 - 2
10 = 10
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The function f, where f(x) = x2 + 6x + 8, is related to function g, where g(x) = 5 f(x-2). What is g(3)?
The function f, where f(x) = x2 + 6x + 8, is related to function g, where g(x) = 5 f(x-2). What is g(3)?
Doing things in an orderly way is a friend to the test-taker.
g(3) = 5 f(3-2)
= 5 f(1)
= 5 \[ 12 + 6**∙**1 + 8\]
= 5 \[ 1 + 6 + 8\]
= 5 \[ 15\]
= 75
Doing things in an orderly way is a friend to the test-taker.
g(3) = 5 f(3-2)
= 5 f(1)
= 5 \[ 12 + 6**∙**1 + 8\]
= 5 \[ 1 + 6 + 8\]
= 5 \[ 15\]
= 75
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A function F is defined as follows:
for x2 > 1, F(x) = 4x2 + 2x – 2
for x2 < 1, F(x) = 4x2 – 2x + 2
What is the value of F(1/2)?
A function F is defined as follows:
for x2 > 1, F(x) = 4x2 + 2x – 2
for x2 < 1, F(x) = 4x2 – 2x + 2
What is the value of F(1/2)?
For F(1/2), x2=1/4, which is less than 1, so we use the bottom equation to solve. This gives F(1/2)= 4(1/2)2 – 2(1/2) + 2 = 1 – 1 + 2 = 2
For F(1/2), x2=1/4, which is less than 1, so we use the bottom equation to solve. This gives F(1/2)= 4(1/2)2 – 2(1/2) + 2 = 1 – 1 + 2 = 2
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If f(x) = _x_2 – 5 for all values x and f(a) = 4, what is one possible value of a?
If f(x) = _x_2 – 5 for all values x and f(a) = 4, what is one possible value of a?
Using the defined function, f(a) will produce the same result when substituted for x:
f(a) = _a_2 – 5
Setting this equal to 4, you can solve for a:
_a_2 – 5 = 4
_a_2 = 9
a = –3 or 3
Using the defined function, f(a) will produce the same result when substituted for x:
f(a) = _a_2 – 5
Setting this equal to 4, you can solve for a:
_a_2 – 5 = 4
_a_2 = 9
a = –3 or 3
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The function 
is defined as 
. What is 
?
The function 
Substitute -1 for 
in the given function.
If you didn’t remember the negative sign, you will have calculated 36. If you remembered the negative sign at the very last step, you will have calculated -36; however, if you did not remember that 
is 1, then you will have calculated 18.
Substitute -1 for 
If you didn’t remember the negative sign, you will have calculated 36. If you remembered the negative sign at the very last step, you will have calculated -36; however, if you did not remember that 
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f(x) = 2x2 + x – 3 and g(y) = 2y – 7. What is f(g(4))?
f(x) = 2x2 + x – 3 and g(y) = 2y – 7. What is f(g(4))?
To evaluate f(g(4)), one must first determine the value of g(4), then plug that into f(x).
g(4) = 2 x 4 – 7 = 1.
f(1) = 2 x 12 + 2 x 1 – 3 = 0.
To evaluate f(g(4)), one must first determine the value of g(4), then plug that into f(x).
g(4) = 2 x 4 – 7 = 1.
f(1) = 2 x 12 + 2 x 1 – 3 = 0.
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What is the value of the function f(x) = 6x2 + 16x – 6 when x = –3?
What is the value of the function f(x) = 6x2 + 16x – 6 when x = –3?
There are two ways to do this problem. The first way just involves plugging in –3 for x and solving 6〖(–3)〗2 + 16(–3) – 6, which equals 54 – 48 – 6 = 0. The second way involves factoring the polynomial to (6x – 2)(x + 3) and then plugging in –3 for x. The second way quickly shows that the answer is 0 due to multiplying by (–3 + 3).
There are two ways to do this problem. The first way just involves plugging in –3 for x and solving 6〖(–3)〗2 + 16(–3) – 6, which equals 54 – 48 – 6 = 0. The second way involves factoring the polynomial to (6x – 2)(x + 3) and then plugging in –3 for x. The second way quickly shows that the answer is 0 due to multiplying by (–3 + 3).
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