Solving Other Functions - SAT Subject Test in Math I
Card 0 of 2
Simplify:
You may assume that 
is a nonnegative real number.
Simplify:
You may assume that
The best way to simplify a radical within a radical is to rewrite each root as a fractional exponent, then convert back.
First, rewrite the roots as exponents.
Multiply the exponents, per the power of a power rule:
The best way to simplify a radical within a radical is to rewrite each root as a fractional exponent, then convert back.
First, rewrite the roots as exponents.
Multiply the exponents, per the power of a power rule:
Compare your answer with the correct one above
Define functions 
and 
.
for exactly one value of 
on the interval 
.
Which of the following statements is correct about 
?
Define functions
Which of the following statements is correct about
Define
Then if 
,
it follows that
,
or, equivalently,
.
By the Intermediate Value Theorem (IVT), if 
is a continuous function, and 
and 
are of unlike sign, then 
for some 
. As a polynomial, 
is a continuous function, so the IVT applies here.
Evaluate 
for each of the following values: 
:
Only in the case of 
does it hold that 
assumes a different sign at both endpoints - 
. By the IVT, 
, and 
, for some 
.
Define
Then if
it follows that
or, equivalently,
By the Intermediate Value Theorem (IVT), if
Evaluate
Only in the case of
Compare your answer with the correct one above