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Composite Functions Worksheet - Page 2

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


Solution:

f(x) = 11x - 4

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

= 11y - 26


Correct answer : (1)
 12.  
If f(x) = 5x + 7 and g(x) = - 9x, 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


Correct answer : (2)
 13.  
If f(x) = 11x and g(x) = 2x - 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


Correct answer : (2)
 14.  
If f(x) = x2 + 2 and g(x) = 2x + 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


Correct answer : (2)
 15.  
If f(x) = - 5x + 3 and g(x) = x2, 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


Correct answer : (4)
 16.  
If f(x) = 3x2 and g(x) = 5x - 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


Correct answer : (4)
 17.  
If f(x) = x2 - 2x, 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


Correct answer : (2)
 18.  
Given f(x) = - 5x and g(x) = 2x2, find the value of the composite function (fog)(x).
a.
- 100x2
b.
- 10x2
c.
100x2
d.
- 10x3


Solution:

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

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

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

= - 10x2


Correct answer : (2)
 19.  
Evaluate the composite function (fog)(x). Given f(x) = 3x + 4 and g(x) = x - 6.
a.
3x - 24
b.
3x - 2
c.
3x2 - 14x - 24
d.
3x - 14


Solution:

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

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

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

= 3x - 14


Correct answer : (4)
 20.  
If f(x) = - 3x2 and g(x) = 2x, evaluate the composite function (gof)(x).
a.
- 6x
b.
- 6x2 + x
c.
- 6x3
d.
- 6x2


Solution:

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

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

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


Correct answer : (4)

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