Free Printable 3.4 Operations on Functions

1.

f(x) = 2x - 2 $\ \ \ \ \ \ \ \ \ \$ h(x) = $x^2$ $\ \ \ \ \ \ \ \ \ \$ k(x) = $x^2$ - 4

g(x) = x + 1 $\ \ \ \ \ \ \ \ \ \$ j(x) = $x^2$ -3x - 4 $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$

Find: $(k-h)(x)$

a)

$-4$

b)

$2x^2-4$

c)

$x^2+4$

d)

$-3$

2.

f(x) = 2x - 2 $\ \ \ \ \ \ \ \ \ \$ h(x) = $x^2$ $\ \ \ \ \ \ \ \ \ \$ k(x) = $x^2$ - 4

g(x) = x + 1 $\ \ \ \ \ \ \ \ \ \$ j(x) = $x^2$ -3x - 4 $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$

Find: $(g\cdot f)(x)$

a)

$2x^2-2$

b)

$2x^3-2x$

c)

$2x^2-4x-2$

d)

$2x^{ }-2$

3.

When f(x) = x²+9 and g(x) = x-9, find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

4.

If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(\frac{f}{g}\right)\left(x\right)$

a)

$\frac{x-1}{5x-2}$

b)

$\frac{5x-2}{x-1}$

c)

$\frac{-1}{3}$

d)

$-3$

5.

Find f(3) + g(2) if f(x)= x+2 and g(x)=5x-1

(a)

6.

Find $(f-g)(2)$ if $f(x)=4x+10$ and $g(x)=3x-7$

(a)

7.

f(x) = 2x and g(x) = 2x-7

Find (f-g)(4).

a)

0

b)

-9

c)

7

d)

-8

8.

Given that

$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

k\left(-7\right)-g\left(8\right)

(a)

9.

Given f(x) = x² + 5 and g(x) = 2x³ - 1,
find (f/g)(-3).

a)

-14/55

b)

14/55

c)

2

d)

-2

10.

f(x) = 2x - 2 $\ \ \ \ \ \ \ \ \ \$ h(x) = $x^2$ $\ \ \ \ \ \ \ \ \ \$ k(x) = $x^2$ - 4

g(x) = x + 1 $\ \ \ \ \ \ \ \ \ \$ j(x) = $x^2$ -3x - 4 $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$

Find: $(f+j)(x)$

a)

$x^2-x-6$

b)

$x^2+x-6$

c)

$x^2-x+6$

d)

$x^2-6$

11.

f(x) = 2x - 2 $\ \ \ \ \ \ \ \ \ \$ h(x) = $x^2$ $\ \ \ \ \ \ \ \ \ \$ k(x) = $x^2$ - 4

g(x) = x + 1 $\ \ \ \ \ \ \ \ \ \$ j(x) = $x^2$ -3x - 4 $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$

Find: $(h\cdot f)(x)$

a)

$2x^2-2x$

b)

$2x^3-2x$

c)

$2x^2-2x^2$

d)

$2x^3-2x^2$

12.

Given the functions, find (g·f)(x).

a)

-8x²+ 2x + 55

b)

-8x²- 2x + 55

c)

-8x²+ 2x - 55

d)

8x²+ 2x + 55

13.

Given the functions, evaluate (g-f)(3).

a)

10

b)

-12

c)

6-6x

d)

18-18x

14.

Given the functions, evaluate (g+f)(2).

a)

12

b)

-12

c)

-2x+16

d)

-4x+32

15.

If $f\left(x\right)\ =\ 3x^2-4$ and $g\left(x\right)=x^2-8x+4$ , then $\left(\frac{f}{g}\right)\left(x\right)=$

a)

$\frac{3x^2-4}{x^2-8x+4}$

b)

$\frac{x^2-8x+4}{3x^2-4}$

c)

$\frac{3x^2-1}{x^2-8x}$

d)

$\frac{1}{-4x}$

3.4 Operations on Functions

Total questions: 15

Worksheet time: 2hrs 36mins

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