# Functions

Read the following SAT test question and then select the correct answer.

All math problems require the same approach.  Read the question carefully and identify the bottom line that you must find.  Assess your options for working the problem, choose the most efficient strategy, and attack the problem.  Always make sure that your answer addresses the bottom line, especially in problems with multiple variables.

If the function f is defined by f(x) = 2x + 3, and if f(a) = 11, what is the value of a?

This question may look complicated because it uses functions, but it can be worked very quickly.  You are given a function using the variable x:
f(x) = 2x + 3

However, your bottom line requires you to solve for another variable: a. Think about the first information you are given in terms of a by substituting an a for every x:
f(a) = 2a + 3

Now plug in your last piece of information, f(a) = 11, and solve the problem using simple arithmetic.
11 = 2a + 3
8 = 2a
4 = a

Your bottom line was to solve for a so you are finished!  Take a look at the answer choices.

(A) 4
(B) 7
(C) 11
(D) 17
(E)25