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Composition of Functions Worksheet

Composition of Functions Worksheet
  • Page 1
 1.  
State the domain of [f o g](x) for f(x) = x - 3 and g(x) = x + 1.
a.
x ≥ 1
b.
x ≥ 0
c.
x ≥ 2
d.
x ≥ 3


Answer: (c)


Correct answer : (3)
 2.  
State the domain of [f o g](x) for f(x) = 2x + 4 and g(x) = 1 x.
a.
x ≠ 0
b.
x ≤ 4
c.
x ≥ 2
d.
x = 0


Answer: (a)


Correct answer : (1)
 3.  
State the domain of [f o g](x) for f(x) = 1 x and g(x) = 2x + 4.
a.
x = 1 2
b.
x ≥ 2
c.
x ≠ - 2
d.
x = - 2


Answer: (c)


Correct answer : (3)
 4.  
Find the domain of [f o g](x) for f(x) = (x2 - 1)and g(x) = x.
a.
(- ∞, - 1] ∩ [1, ∞)
b.
[ 0, ∞)
c.
(- ∞, - 1] ∪ [1, ∞)
d.
(0, 1)


Answer: (b)


Correct answer : (2)
 5.  
State the domain of [f o g](x) for f(x) = x - 4 and g(x) = x + 1.
a.
x ≥ 2
b.
x ≤ 3
c.
x ≤ 2
d.
x ≥ 3


Answer: (d)


Correct answer : (4)
 6.  
Evaluate the composite function (fog)(x), given f(x) = 4x + 6 and g(x) = x - 9.
a.
4x - 54
b.
4x - 3
c.
4x - 30
d.
4x2 - 30x - 54


Answer: (c)


Correct answer : (3)
 7.  
If f(x) = 3x2 and g(x) = 5x + 2, then find (gof)(x).
a.
15x3 + 6x2
b.
15x + 6
c.
6x2
d.
15x2 + 2


Answer: (d)


Correct answer : (4)
 8.  
If f(x) = 2x + 4 and g(x) = 5x2, evaluate the composite function (fog)(x2).
a.
(10x2 + 4)2
b.
10x2 + 4
c.
10x4 + 4
d.
(10x + 4)2


Answer: (c)


Correct answer : (3)
 9.  
If f(x) = 5x - 9 and g(x) = 5x3, find the value of the composite function (gof)(3x).
a.
x3 - 15
b.
(15x - 27)3
c.
15(x3 - 5)
d.
5(15x - 9)3


Answer: (d)


Correct answer : (4)
 10.  
If f(x) = - 2x4 and g(x) = 4x - 6, then find (fog)(x - 1).
a.
2(4x - 6)4 - 1
b.
- 4(x - 1)4(2x - 5)
c.
- 2(x4 - 1)
d.
- 2(4x - 10)4


Answer: (d)


Correct answer : (4)

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