All SAT II Math I Resources
Example Question #1 : Solving Other Functions
You may assume that is a nonnegative real number.
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:
Example Question #2 : Solving Other Functions
Define functions and .
for exactly one value of on the interval .
Which of the following statements is correct about ?
Then if ,
it follows that
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 .