#### Solved Examples and Worksheet for Operations with Functions

Q1Find a rule for the function (f - g)(x), if f(x) = xx2 - 9, g(x) = 3x2 - 9.

A. (f - g)(x) = 13 - x
B. (f - g)(x) = -1x + 3
C. (f - g)(x) = 1x - 3
D. (f - g)(x) = 1x + 3

Step: 1
f(x) = xx2 - 9, g(x) = 3x2 - 9
[Original functions.]
Step: 2
(f - g)(x) = f(x) - g(x)
[Write the rule for the difference of functions.]
Step: 3
= xx2 - 9 - 3x2 - 9
[Substitute the values for f(x) and g(x).]
Step: 4
= x - 3x2 - 9
[Subtract.]
Step: 5
= x - 3(x -  3)(x + 3)
[Factor.]
Step: 6
= 1x + 3
[Simplify.]
Step: 7
(f - g)(x) = 1x + 3
Correct Answer is :   (f - g)(x) = 1x + 3
Q2If f(x) = 3x + 6 and g(x) = 3x + 9, find (f + g)(x).

A. 6x + 16
B. 6x + 15
C. 6x + 13
D. 9x + 12
E. 6x + 14

Step: 1
(f + g)(x) = f(x) + g(x).
Step: 2
= 3x + 6 + 3x + 9.
Step: 3
= 6x + 15.
Correct Answer is :   6x + 15
Q3If f (x) = x2 - 15x + 8, g (x) = x2 - 21x + 10, what is the value of (f - g)(x)?

A. 6x
B. 6x + 2
C. - 6x - 2
D. - 6x + 2
E. 6x - 2

Step: 1
Given, f (x) = x2 - 15x + 8 and g (x) = x2 - 21x + 10.
Step: 2
(f - g)(x) = f (x) - g (x) = x2 - 15x + 8 - (x2 - 21x + 10)
Step: 3
= x2 - 15x + 8 - x2 + 21x - 10 = 6x - 2
Correct Answer is :   6x - 2
Q4If f (x) = 2x, g (x) = x4 + 4, what is the value of (f × g)(x)?
A. 2x5
B. 2x5 + 8x
C. 2x + x4 + 2
D. x4 + 8
E. 2x4 + 8x

Step: 1
Given, f (x) = 2x and g (x) = x4 + 4.
Step: 2
(f × g)(x) = f (x) × g (x)
Step: 3
= 2x × (x4 + 4) = 2x5 + 8x
Correct Answer is :   2x5 + 8x
Q5If f (x) = 8x, g (x) = x2, what is the value of (fg)(x)?

A. x2
B. 8x
C. 8x3
D. 8x
E. 8x + x2

Step: 1
Given, f (x) = 8x and g (x) = x2
Step: 2
(fg)(x) = f(x)g(x), g (x) ≠ 0
Step: 3
= 8xx2, g (x) ≠ 0
Step: 4
= 8x
Q6If f(x) = - 2x2 + 4x - 9 and g(x) = x2 + 8, then find (f - g)(x).

A. - 3x2 + 4x - 17
B. 3x2 + 4x - 17
C. - x2 + 4x - 17
D. - 3x2 + 4x + 17

Step: 1
(f - g)(x) = f(x) - g(x)
Step: 2
= - 2x2 + 4x - 9 - (x2 + 8)
[Substitute the values.]
Step: 3
= - 2x2 + 4x - 9 - x2 - 8
Step: 4
= - 3x2 + 4x - 17
[Simplify.]
Correct Answer is :   - 3x2 + 4x - 17
Q7If f(x) = - 7x5 - x2 + x + 10 and g(x) = - x2 + x, then find (f - g)(x).

A. 7x5 + 10
B. - 7x5 + 2x2 + 10
C. - 7x5 + 10
D. - 7x5 + x + 10

Step: 1
(f - g)(x) = f(x) - g(x)
Step: 2
= - 7x5 - x2 + x + 10 - (- x2 + x)
[Substitute the values.]
Step: 3
= - 7x5 - x2 + x + 10 + x2 - x
Step: 4
= - 7x5 + 10
[Simplify.]
Correct Answer is :   - 7x5 + 10
Q8Find (f - g)(x) for f(x) = x+ 3 and g(x) = x2 + x - 1.
A. - x2 + 4
B. x2 - 4
C. - x2 - x + 3
D. - x2 - 2x + 4

Step: 1
(f - g)(x) = f(x) - g(x)
[Subtraction of functions.]
Step: 2
= (x + 3) - (x2 + x - 1)
[f(x) = x+ 3 and g(x) = x2 + x - 1.]
Step: 3
= - x2 + 4
[Simplify.]
Correct Answer is :   - x2 + 4
Q9If f(x) = 11x + 3 and g(x) = 11x + 7, find (f + g)(x).

A. 6x + 7
B. x + 10
C. 121x + 10
D. 22x + 10

Step: 1
(f + g)(x) = f(x) + g(x)
Step: 2
= 11x + 3 + 11x + 7
Step: 3
= 22x + 10
Correct Answer is :   22x + 10
Q10If f(x) = 12x - 9 and g(x) = 12x + 21, find (f + g)(x).
A. 12x + 12
B. 24x + 12
C. 6x - 12
D. x + 12

Step: 1
(f + g)(x) = f(x) + g(x)
Step: 2
= 12x - 9 + 12x + 21
Step: 3
= 24x + 12
Correct Answer is :   24x + 12
Q11If f (x) = 2x, g (x) = x6 + 8, what is the value of (f × g)(x)?
A. 2x7 + 16x
B. x7 + 2x
C. 2x6 + 16x
D. 2x8 + 16x

Step: 1
Given, f (x) = 2x and g (x) = x6 + 8.
Step: 2
(f × g)(x) = f (x) × g (x)
Step: 3
= 2x × (x6 + 8) = 2x7 + 16x
Correct Answer is :   2x7 + 16x
Q12If f (x) = 9x, g (x) = x5, what is the value of (fg)(x)?
A. 9x
B. x5
C. 9x6
D. 9x4

Step: 1
Given, f (x) = 9x and g (x) = x5
Step: 2
(fg)(x) = f(x)g(x), g (x) ≠ 0
Step: 3
= 9xx5
Step: 4
= 9x4
Q13If f (x) = 7x2, g (x) = x3 + 8, what is the value of (f × g)(x)?
A. 7x2 + 56x
B. 7x6 + 56x2
C. 7x5 + 8
D. 7x5 + 56x2

Step: 1
Given, f (x) = 7x2 and g (x) = x3 + 8.
Step: 2
(f × g)(x) = f (x) × g (x)
Step: 3
= 7x2 × (x3 + 8) = 7x5 + 56x2
Correct Answer is :   7x5 + 56x2
• Function