﻿ COMBINING FUNCTIONS - Overview - Functions - REVIEW OF MAJOR TOPICS - SAT SUBJECT TEST MATH LEVEL 2 ﻿

## CHAPTER 1Functions

### COMBINING FUNCTIONS

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

 Sum function ( f + g)(x) = f (x) + g(x) Difference function ( f – g)(x) = f (x) – g(x) Product function Quotient function if and only if Composition of functions

EXAMPLE

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

(A) (g)(x)

(B) (– g)(x)

(C· g (x)

(D)

(E) ( g)(x)

(F) ( f )(x)

SOLUTIONS

(A)

(B)

(C)

(D)

(E)

(F)

 TIP        (f  g)(x) and (g  f)(x) need not be the same!

EXERCISES

1.       If f(x) = 3x2 – 2+ 4, f(–2) =

(A) –12

(B) –4

(C) –2

(D) 12

(E) 20

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

(A) 3

(B) 9

(C) 27

(D) 31

(E) none of the above

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

(A) 4 – x

(B) x

(C) 2– 2

(D) 4x

(E) x2

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

(A) 0

(B) 1

(C) 3

(D) both ±1

(E) no values

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

(A) 0

(B) 1

(C) 2

(D) 6

(E) 8

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

(A) −6

(B)

(C)

(D)

(E) 2

7.       If f(x) = ex 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

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