﻿ Composite Functions Worksheet - Page 2 | Problems & Solutions

# Composite Functions Worksheet - Page 2

Composite Functions Worksheet
• Page 2
11.
If $f$($x$) = 11$x$ - 4, then find $f$($y$ - 2).
 a. 11$y$ - 26 b. 11$y$ - 22 c. 11$y$ - 1 d. 11$y$ - 2

#### Solution:

f(x) = 11x - 4

f(y - 2) = 11(y - 2) - 4
[Substitute the values.]

= 11y - 26

12.
If $f$($x$) = 5$x$ + 7 and $g$($x$) = - 9$x$, evaluate the composite function $g$[$f$(2)].
 a. -218 b. - 153 c. 17 d. 9

#### Solution:

f(x) = 5x + 7
[First find f(2).]

f(2) = 10 + 7 = 17
[Substitute the values.]

g(x) = - 9x
[Then find g[f (2)].]

g[f(2)] = g(17) = - 9(17) = - 153

13.
If $f$($x$) = 11$x$ and $g$($x$) = 2$x$ - 1, find the value of $g$[$f$(- 2)].
 a. - 11 b. - 45 c. 22 d. - 22

#### Solution:

f(x) = 11x
[First find f(- 2).]

f(- 2) = 11(- 2) = - 22
[Substitute the values.]

g(x) = 2x - 1
[Then find g[f(- 2)].]

g[f(- 2)] = g(- 22) = 2(- 22) - 1 = - 45

14.
If $f$($x$) = $x$2 + 2 and $g$($x$) = 2$x$ + 1, find the value of $f$[$g$(3)].
 a. 7 b. 51 c. 11 d. 3

#### Solution:

g(x) = 2x + 1
[First find g(3).]

g(3) = 6 + 1 = 7
[Substitute the values.]

f(x) = x2 + 2
[Then find f[g(3)].]

f[g(3)] = f(7) = (7)2 + 2 = 51

15.
If $f$($x$) = - 5$x$ + 3 and $g$($x$) = $x$2, evaluate the composite function $f$[$g$(- 5)].
 a. 3 b. 25 c. 128 d. -122

#### Solution:

g(x) = x2
[First find g (- 5).]

g(- 5) = (- 5)2 = 25
[Substitute the values.]

f(x) = - 5x + 3
[Then find f[ g(- 5)].]

f[g(- 5)] = f(25) = - 5(25) + 3 = -122

16.
If $f$($x$) = 3$x$2 and $g$($x$) = 5$x$ - 2, evaluate $f$[$g$($x$)] for $x$ = - 3, 0, 3.
 a. 12, - 2, - 507 b. - 867, 12, 13 c. 17, 12, 507 d. 867, 12, 507

#### Solution:

g(x) = 5x - 2

g(- 3) = 5(- 3) - 2 = - 17
[Substitute the values.]

g(0) = 5(0) - 2 = - 2
[Substitute the values.]

g(3) = 5(3) - 2 = 13
[Substitute the values.]

f(x) = 3x2

f[g(- 3)] = f[- 17] = 3(- 17)2 = 867

f[g(0)] = f[- 2] = 3(- 2)2 = 12

f[g(3)] = f[13] = 3(13)2 = 507

17.
If $f$($x$) = $x$2 - 2$x$, $g$($x$) = 1 - $x$, evaluate $g$[$f$($x$)] for $x$ = - 1, 0, 1.
 a. -2, 1, 0 b. -2, 1, 2 c. 4, 0, 2 d. 2, 2, 0

#### Solution:

f(x) = x2 - 2x

f(- 1) = (- 1)2 - 2(- 1) = 3
[Substitute the values.]

f(0) = (0)2 - 2(0) = 0
[Substitute the values.]

f(1) = (1)2 - 2(1) = -1
[Substitute the values.]

g(x) = 1 - x

g[f(- 1)] = g[3] = 1 -3 = -2

g[f(0)] = g[0] = 1 - 0 = 1

g[f(1)] = g(-1) = 1 - (-1) = 2

18.
Given $f$($x$) = - 5$x$ and $g$($x$) = 2$x$2, find the value of the composite function ($f$o$g$)($x$).
 a. - 100$x$2 b. - 10$x$2 c. 100$x$2 d. - 10$x$3

#### Solution:

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

= f[2x2]
[Substitute the values.]

= - 5(2x2)
[Substitute the values.]

= - 10x2

19.
Evaluate the composite function ($f$o$g$)($x$). Given $f$($x$) = 3$x$ + 4 and $g$($x$) = $x$ - 6.
 a. 3$x$ - 24 b. 3$x$ - 2 c. 3$x$2 - 14$x$ - 24 d. 3$x$ - 14

#### Solution:

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

= f[x - 6]
[Substitute the values.]

= 3(x - 6) + 4
[Substitute the values.]

= 3x - 14

20.
If $f$($x$) = - 3$x$2 and $g$($x$) = 2$x$, evaluate the composite function ($g$o$f$)($x$).
 a. - 6$x$ b. - 6$x$2 + $x$ c. - 6$x$3 d. - 6$x$2

#### Solution:

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

= g[- 3x2]
[Substitute the values.]

= 2(- 3x2) = - 6 x2
[Substitute the values.]