Understanding Inverse Functions - High School Math
Card 0 of 3
Let 
. What is 
?
Let
We are asked to find 
, which is the inverse of a function.
In order to find the inverse, the first thing we want to do is replace f(x) with y. (This usually makes it easier to separate x from its function.).
Next, we will swap x and y.
Then, we will solve for y. The expression that we determine will be equal to 
.
Subtract 5 from both sides.
Multiply both sides by -1.
We need to raise both sides of the equation to the 1/3 power in order to remove the exponent on the right side.
We will apply the general property of exponents which states that 
.
Laslty, we will subtract one from both sides.
The expression equal to y is equal to the inverse of the original function f(x). Thus, we can replace y with 
.
The answer is 
.
We are asked to find
In order to find the inverse, the first thing we want to do is replace f(x) with y. (This usually makes it easier to separate x from its function.).
Next, we will swap x and y.
Then, we will solve for y. The expression that we determine will be equal to
Subtract 5 from both sides.
Multiply both sides by -1.
We need to raise both sides of the equation to the 1/3 power in order to remove the exponent on the right side.
We will apply the general property of exponents which states that
Laslty, we will subtract one from both sides.
The expression equal to y is equal to the inverse of the original function f(x). Thus, we can replace y with
The answer is
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What is the inverse of 
?
What is the inverse of
The inverse of 
requires us to interchange 
and 
and then solve for 
.
Then solve for 
:
The inverse of
Then solve for
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If 
, what is 
?
If
To find the inverse of a function, exchange the 
and 
variables and then solve for 
.
To find the inverse of a function, exchange the
Compare your answer with the correct one above