﻿ Operation of Functions Worksheet | Problems & Solutions

# Operation of Functions Worksheet

Operation of Functions Worksheet
• Page 1
1.
Find the next term of the geometric sequence: $\frac{1}{2}$ , $\frac{1}{3}$ , $\frac{2}{9}$ , $\frac{4}{27}$ ,.....
 a. $\frac{2}{3}$ b. $\frac{8}{18}$ c. $\frac{8}{81}$ d. $\frac{4}{28}$

2.
Find the area of a sector with a diameter of 8 m and a central angle of 90°.
 a. 16π m2 b. 8π m2 c. 4π m2 d. 12π m2

#### Solution:

Area of a sector = central angle360 × πr2

= 90360 × π (4 m)2
[Substitute the values.]

Area of the sector = 4π m2
[Simplify.]

3.
Find the area of a sector with a radius of 6 in. and a central angle of 160°.
 a. 6π in.2 b. 16π in.2 c. $\frac{6\pi }{5}$ in.2 d. 19π in.2

#### Solution:

Area of a sector = central angle360 × πr2

= 160360 × π(6 in.)2
[Substitute the values.]

Area of the sector = 16π in.2
[Simplify.]

4.
Find the area of a sector with a radius of 3 ft and a central angle of 45°.
 a. $\frac{7\pi }{5}$ ft3 b. $\frac{9\pi }{8}$ ft2 c. $\frac{25\pi }{6}$ ft2 d. $\frac{5\pi }{8}$ ft2

#### Solution:

Area of a sector = central angle360 × πr2

= 45360 × π(3 ft)2
[Substitute the values.]

Area of the sector = 9π8 ft2
[Simplify.]

5.
Find the area of a sector with radius of 5 cm and a central angle of 40°.
 a. 8π cm2 b. $\frac{25\pi }{9}$ cm2 c. 5π cm2 d. $\frac{7\pi }{2}$ cm2

#### Solution:

Area of a sector = central angle360 × πr2

= 40360 × π(5 cm)2
[Substitute the values.]

Area of the sector = 25π9 cm2
[Simplify.]

6.
Find the area of a sector with radius of 4 cm and a central angle of 60°.
 a. $\frac{6\pi }{5}$ cm2 b. 4π cm2 c. $\frac{8\pi }{3}$ cm2 d. $\frac{3\pi }{8}$ cm2

#### Solution:

Area of a sector = central angle360 × πr2

= 60360 × π(4 cm)2
[Substitute the values.]

Area of the sector = 8π3 cm2
[Simplify.]

7.
Find ($f$ + $g$)(1), if $f$($x$) = - 2$x$ and $g$($x$) = ($x$ - 1).
 a. - 2 b. 2 c. 1

8.
Evaluate the function ($\frac{f}{g}$)(- 2) when $f$($x$) = ($x$ + 1) and $g$($x$) = $\frac{x}{2}$.
 a. - 1 b. 1 c. 4

9.
Find ($\mathrm{fg}$)(- 1) when $f$($x$) = $\frac{x}{1+3x}$ and $g$($x$) = 1 - 2$x$.
 a. 5 b. 6 c. $\frac{3}{2}$ d. $\frac{1}{2}$

Find the value of ($f$ - $g$)(1) when $f$($x$) = $\frac{2x+5}{x+1}$ and $g$($x$) = $x$ - 1.
 a. $\frac{2}{7}$ b. 1 c. $\frac{7}{2}$ d. 2