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Composite Functions Worksheet - Page 3

Composite Functions Worksheet
  • Page 3
 21.  
If f(x) = 3x2 and g(x) = 5x + 2, then find (gof)(x).
a.
15x + 6
b.
15x3 + 6x2
c.
15x2 + 2
d.
6x2


Solution:

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

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

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

= 15x2 + 2


Correct answer : (3)
 22.  
If f(x) = 3x + 3 and g(x) = 4x2, evaluate the composite function (fog)(x2).
a.
12x2 + 3
b.
(12x2 + 3)2
c.
(12x + 3)2
d.
12x4 + 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


Correct answer : (4)
 23.  
If f(x) = 2x - 7 and g(x) = 2x3, find the value of the composite function (gof)(3x).
a.
6(x3 - 2)
b.
2(6x - 7)3
c.
(6x - 21)3
d.
x3 - 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.]


Correct answer : (2)
 24.  
If f(x) = - 2x4 and g(x) = 4x - 6, then find (fog)(x - 1).
a.
2(4x - 6)4 - 1
b.
- 2(x4 - 1)
c.
- 2(4x - 10)4
d.
- 4(x - 1)4(2x - 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.]


Correct answer : (3)
 25.  
If f(x) = 7x - 4 and g(x) = 1 + 2x, find (gof)(- 2x).
a.
- 28x - 2
b.
- 28x + 6
c.
28x + 8
d.
- 28x - 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.]


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


Correct answer : (3)
 27.  
If g(x) = 4x + 2, then find the composite function (gog)(x + 1).
a.
4x + 2
b.
4x + 24
c.
16x + 26
d.
16x + 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


Correct answer : (3)
 28.  
If f(x) = 5x - 3, then find the value of f(3 +  h) - f(3)h, 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


Correct answer : (2)

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