﻿ Composite Functions Worksheet | Problems & Solutions

# Composite Functions Worksheet

Composite Functions Worksheet
• Page 1
1.
If $f$ ($x$) = 7$x$ - 2 and $g$ [$f$ ($x$)] = 3$x$2 - 70 then find $g$ (33).
 a. 70 b. 33 c. 75 d. 5

#### Solution:

g [f (x)] = 3x2 - 70

To find g(33), first find for what value of x, f (x) = 33

7x - 2 = 33

7x = 35

x = 5

g [f(x)] = 3x2 - 70

g [f(5)] = 3(5)2 - 70
[Replace x with 5.]

g (33) = 3(25) - 70 = 5
[f (5) = 7(5) - 2 = 33.]

2.
If $g$ ($x$) = 4$x$ + 4 and $f$ ($x$) = $x$2 - 64 then for what values of $x$ the expression ($f$o$g$)($x$) equals to zero?
 a. -1 , 3 b. 4, - 64 c. 1 , - 3 d. √63

#### Solution:

(fog) (x) = f[g(x)]

= f[4x + 4]
[Replace g (x) with 4x + 4.]

= (4x + 4)2 - 64
[Replace x with 4x + 4 in f (x).]

(fog)(x) = 0

(4x + 4)2 - 64 = 0

(4x + 4)2 = 64

4x + 4 = ± 8

4x + 4 = 8 or 4x + 4 = - 8

4x = 4 or 4x = - 12

x = 1 or x = - 3

So, the expression (fog)(x) equals zero when x = 1 , - 3

3.
If $f$($x$) = - 4$x$2 and $g$($x$) = 2$x$ - 6, then find ($f$o$g$)($x$ - 3).
 a. 4($x$ - 3)2 - 2 b. - 4(2$x$ - 12)2 c. - (2$x$ - 10)2 d. - 4$x$2 - 10

#### Solution:

g(x) = 2x - 6

g(x - 3) = 2(x - 3) - 6
[Substitute the values.]

= 2x - 6 - 6

= 2x - 12

f(x) = - 4x2

(fog)(x - 3) = f[g(x - 3)]

= f[2x - 12]

= - 4(2x - 12)2
[Substitute the values.]

4.
If $f$($x$) = 2$x$ + 3, then what is the value of $f$(3)?
 a. 3 b. 9 c. 18 d. 14

#### Solution:

f(x) = 2x + 3

f(3) = 2(3) + 3 = 9
[Substitute the values.]

5.
If $f$($x$) = 2$x$ + 4, then what is the value of $f$(5)?
 a. 17 b. 14 c. 13 d. 12

#### Solution:

f(x) = 2x + 4

f(5) = 2(5) + 4 = 14
[Substitute the values.]

6.
If $f$($x$) = 3$x$2 - 4, then find the value of $f$(- 5).
 a. 71 b. -4 c. 25 d. 75

#### Solution:

f(x) = 3x2 - 4

f(- 5) = 3(- 5)2 - 4 = 71
[Substitute the values.]

7.
Evaluate the function $g$($x$) = 2$x$3 - 7 for $x$ = - 1, 0, 5.
 a. - 2, - 7, 9 b. - 9, - 7, 243 c. - 9, - 7, 1 d. 9, - 1, 243

#### Solution:

g(x) = 2x3 - 7

g(- 1) = 2(- 1)3 - 7 = - 9
[Substitute the values.]

g(0) = 2(0)3 - 7 = - 7
[Substitute the values.]

g(5) = 2(5)3 - 7 = 243
[Substitute the values.]

8.
Evaluate the function $h$($x$) = 4$x$ + 10 for $x$ = - 4, 0, 4, $x$.
 a. 4, 10, 10, 4$x$ + 10 b. -6, 26, 26, 4$x$ + 10 c. -6, 10, 26, 4$x$ + 10 d. -6, 10, 28, 4$x$ + 10

#### Solution:

h(x) = 4x + 10

h(- 4) = 4(- 4) + 10 = -6
[Substitute the values.]

h(0) = 4(0) + 10 = 10
[Substitute the values.]

h(4) = 4(4) + 10 = 26
[Substitute the values.]

h(x) = 4(x) + 10 = 4x + 10
[Substitute the values.]

9.
Evaluate the function $f$($x$) = 5$x$ - 8 for $x$ = - 5, 0, 5.
 a. - 35, - 8, 33 b. - 33, - 8, 17 c. 0, 8, 17 d. 0, - 8, 0

#### Solution:

f(x) = 5x - 8

f(- 5) = - 25 - 8 = - 33
[Substitute the values.]

f(0) = 0 - 8 = - 8
[Substitute the values.]

f(5) = 25 - 8 = 17
[Substitute the values.]

10.
If $g$($x$) = $x$2 - 4$x$ + 3, then evaluate $g$(- 4).
 a. 19 b. - 16 c. 39 d. 35

#### Solution:

g(x) = x2 - 4x + 3

g(- 4) = (- 4)2 - 4(- 4) + 3
[Substitute the values.]

= 16 + 16 + 3 = 35