﻿ Composite Functions Worksheet - Page 3 | Problems & Solutions

# Composite Functions Worksheet - Page 3

Composite Functions Worksheet
• Page 3
21.
If $f$($x$) = 3$x$2 and $g$($x$) = 5$x$ + 2, then find ($g$o$f$)($x$).
 a. 15$x$ + 6 b. 15$x$3 + 6$x$2 c. 15$x$2 + 2 d. 6$x$2

#### Solution:

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

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

= 5(3x2) + 2
[Substitute the values.]

= 15x2 + 2

22.
If $f$($x$) = 3$x$ + 3 and $g$($x$) = 4$x$2, evaluate the composite function ($f$o$g$)($x$2).
 a. 12$x$2 + 3 b. (12$x$2 + 3)2 c. (12$x$ + 3)2 d. 12$x$4 + 3

#### Solution:

( fog)(x2) = f[g(x2)]

g(x) = 4x2
[First find g(x2).]

g(x2) = 4(x2)2 = 4x4
[Substitute the values.]

So, f[g(x2)] = f[4x4].

= 3(4x4) + 3
[Substitute the values.]

= 12x4 + 3

23.
If $f$($x$) = 2$x$ - 7 and $g$($x$) = 2$x$3, find the value of the composite function ($g$o$f$)(3$x$).
 a. 6($x$3 - 2) b. 2(6$x$ - 7)3 c. (6$x$ - 21)3 d. $x$3 - 6

#### Solution:

f(x) = 2x - 7

f(3x) = 6x - 7
[Substitute the values.]

g(x) = 2x3

(gof)(3x) = g[f(3x)]

= g[6x - 7]
[Substitute the values.]

= 2(6x - 7)3
[Substitute the values.]

24.
If $f$($x$) = - 2$x$4 and $g$($x$) = 4$x$ - 6, then find ($f$o$g$)($x$ - 1).
 a. 2(4$x$ - 6)4 - 1 b. - 2($x$4 - 1) c. - 2(4$x$ - 10)4 d. - 4($x$ - 1)4(2$x$ - 5)

#### Solution:

g(x) = 4x - 6

g(x - 1) = 4(x - 1) - 6
[Substitute the values.]

= 4x - 4 - 6

= 4x - 10

f(x) = - 2x4

(fog)(x - 1) = f[g(x - 1)]

= f[4x - 10]

= - 2(4x - 10)4
[Substitute the values.]

25.
If $f$($x$) = 7$x$ - 4 and $g$($x$) = 1 + 2$x$, find ($g$o$f$)(- 2$x$).
 a. - 28$x$ - 2 b. - 28$x$ + 6 c. 28$x$ + 8 d. - 28$x$ - 7

#### Solution:

f(x) = 7x - 4

f(- 2x) = 7(- 2x) - 4
[Substitute the values.]

f(- 2x) = - 14x - 4

g(x) = 1 + 2x

( gof)(- 2x) = g[f(- 2x)]

= g[- 14x - 4]

= 1 + 2(- 14x - 4) = - 28x - 7
[Substitute the values.]

26.
If $f$($x$) = 4$x$ - 5, then find the composite function ($f$o$f$)(8$x$).
 a. (4$x$ - 5)2 b. 4$x$ - 20 c. 128$x$ - 25 d. 128$x$ - 20

#### Solution:

= f[4(8x) - 5]
(fof)(8x) = f[f(8x)]

= f[32x - 5]
[Substitute the values.]

= 4(32x - 5) - 5
[Substitute the values.]

= 128x - 25

27.
If $g$($x$) = 4$x$ + 2, then find the composite function ($g$o$g$)($x$ + 1).
 a. 4$x$ + 2 b. 4$x$ + 24 c. 16$x$ + 26 d. 16$x$ + 24

#### Solution:

g(x) = 4x + 2

g(x + 1) = 4(x + 1) + 2 = 4x + 6
[Substitute the values.]

( gog)(x + 1) = g[g(x + 1)]

= g[4x + 6]

= 4(4x + 6) + 2
[Substitute the values.]

= 16x + 26

28.
If $f$($x$) = 5$x$ - 3, then find the value of , $h$ ≠ 0.
 a. 12 b. 5 c. 4 d. 15

#### Solution:

f(x) = 5x - 3

f(3) = 5(3) - 3 = 12
[Substitute the values.]

f(3 + h) = 5(3 + h) - 3 = 5h + 12
[Substitute the values.]

f(3 + h) - f(3)h = 5h + 12 - 12h

= 5hh

= 5