Composite Functions Worksheet

Composite Functions Worksheet
  • Page 1
 1.  
If f (x) = 7x - 2 and g [f (x)] = 3x2 - 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.]


Correct answer : (4)
 2.  
If g (x) = 4x + 4 and f (x) = x2 - 64 then for what values of x the expression (fog)(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


Correct answer : (3)
 3.  
If f(x) = - 4x2 and g(x) = 2x - 6, then find (fog)(x - 3).
a.
4(x - 3)2 - 2
b.
- 4(2x - 12)2
c.
- (2x - 10)2
d.
- 4x2 - 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.]


Correct answer : (2)
 4.  
If f(x) = 2x + 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.]


Correct answer : (2)
 5.  
If f(x) = 2x + 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.]


Correct answer : (2)
 6.  
If f(x) = 3x2 - 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.]


Correct answer : (1)
 7.  
Evaluate the function g(x) = 2x3 - 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.]


Correct answer : (2)
 8.  
Evaluate the function h(x) = 4x + 10 for x = - 4, 0, 4, x.
a.
4, 10, 10, 4x + 10
b.
-6, 26, 26, 4x + 10
c.
-6, 10, 26, 4x + 10
d.
-6, 10, 28, 4x + 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.]


Correct answer : (3)
 9.  
Evaluate the function f(x) = 5x - 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.]


Correct answer : (2)
 10.  
If g(x) = x2 - 4x + 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


Correct answer : (4)

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