PSAT Math Multiple-Choice Question 54: Answer and Explanation

Question: 54

If f(x) = , what is the value of ?

• A.
• B.
• C.
• D.

Correct Answer: D

Explanation:

D

The question asks for the value of an expression made of two functions. To solve, first evaluate each function. In function notation, the number inside the parentheses is the x-value that goes into the function, and the value that comes out of the function is the y-value. Start with the top function. Plug x = 8 into the f(x) function to get f(8) = 8. Remember the rules of exponents: when a value is raised to a negative exponent, take the reciprocal and make the exponent positive. So, 8 = . When dealing with fractional exponents, remember that the numerator raises the base to a power and the denominator takes a root of the base. So, . Next, find f(3). Plug x = 3 into the f(x) function to get f(3) = 3. This is equivalent to . Simplifying this expression any further will give a complex decimal, so it is easier to leave it as a fraction, = . The correct answer is (D).