SAT SUBJECT TEST MATH LEVEL 2

PART 2

REVIEW OF MAJOR TOPICS

CHAPTER 1
Functions

1.1 Overview

COMBINING FUNCTIONS

Given two functions, f and g, five new functions can be defined:

EXAMPLE

If f(x) = 3x – 2 and g(x) = x² – 4, write an expression for each of the following functions:

 (A) (f + g)(x)

 (B) (f – g)(x)

 (C) f · g (x)

 (D)

 (E) (f g)(x)

 (F) (g f )(x)

SOLUTIONS

  (A)

  (B)

  (C)

  (D)

  (E)

  (F)

EXERCISES

1. If f(x) = 3x² – 2x + 4, f(–2) =

  (A) –12

  (B) –4

  (C) –2

  (D) 12

  (E) 20

2. If f(x) = 4x – 5 and g(x) = 3^x, then f(g(2)) =

  (A) 3

  (B) 9

  (C) 27

  (D) 31

  (E) none of the above

3. If f(g(x)) = 4x² – 8x and f(x) = x² – 4, then g(x) =

  (A) 4 – x

  (B) x

  (C) 2x – 2

  (D) 4x

  (E) x²

4. What values must be excluded from the domain of (x) if f(x) = 3x² – 4x + 1 and g(x) = 3x² – 3?

  (A) 0

  (B) 1

  (C) 3

  (D) both ±1

  (E) no values

5. If g(x) = 3x + 2 and g(f(x)) = x, then f(2) =

  (A) 0

  (B) 1

  (C) 2

  (D) 6

  (E) 8

6. If p(x) = 4x – 6 and p(a) = 0, then a =

  (A) −6

  (B)

  (C)

  (D)

  (E) 2

7. If f(x) = e^x and g(x) = sin x, then the value of (f g)( ) is

  (A) –0.01

  (B) –0.8

  (C) 0.34

  (D) 1.8

  (E) 2.7