SAT II Math I : Solving Other Functions

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

Example Question #1 : Solving Other Functions


You may assume that  is a nonnegative real number.

Possible Answers:

Correct answer:


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 ?

Possible Answers:

Correct answer:



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 .

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