Free Printable MC 8.3 Function Operation and Composition

1.

Given f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

2.

f(x) = 4x+8
g(x) = x+3,
Find f(x) * g(x)

a)

4x²+24

b)

4x²+20x+24

c)

4x²+12x+24

d)

4x²+4x+24

3.

f(x) = x²+9
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.

f(x)=3x²+1
g(x)=4x+5
What is (f+g)(2)

a)

13

b)

0

c)

26

d)

6x²+8x+12

5.

g(x)=3x+4
h(x)=3x-1
Find g(h(x))

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

6.

When f(x) = 2x and g(x) = x²+3 , find f(g(x)).

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

7.

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of f(g(4)).

a)

182

b)

40

c)

61

d)

None of the Above

8.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

a)

16

b)

4

c)

-4

d)

None of these.

9.

p(x) = 3x + 4
q(x) = 2x²
Find q(p(-2))

a)

8

b)

-8

c)

28

d)

None of these.

10.

Find f(2).

a)

-2

b)

-18

c)

24

d)

6

11.

Find g(5)

a)

3375

b)

375

c)

25

d)

45

12.

g(4x)

a)

1728x³

b)

12x³

c)

192x³

d)

36x³

13.

Find f[g(5)]

a)

30

b)

242

c)

92

d)

2

14.

f(g(x))

a)

3x - 16

b)

3x - 2

c)

3x - 26

d)

4x - 2

15.

f(x) = x²+9
g(x) = x-9
Find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

16.

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of f(g(4)).

a)

182

b)

40

c)

61

d)

None of the Above

17.

g(a) = 4a + 1

h(a) = -3a + 2

Find g(h(1))

a)

3

b)

-3

c)

21

d)

-21

18.

f(n)=2n+1
g(n)=3n
Find f(n)+g(n)

a)

5n+1

b)

-5n+1

c)

-2n+1

d)

-6n-1

19.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(3\right)\right)$

a)

34

b)

71

c)

35

d)

142

20.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $g\left(f\left(-1\right)\right)$

a)

2

b)

15

c)

7

d)

-9

21.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(x\right)\right)$

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

22.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $g\left(f\left(x\right)\right)$

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

23.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(f\circ g\right)\left(2\right)$

a)

$\frac{1}{4}$

b)

$\frac{1}{8}$

c)

$\frac{7}{2}$

d)

8

24.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ g\right)\left(-4\right)$

a)

44

b)

-40

c)

-30

d)

-28

25.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ f\right)\left(x\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

26.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $f\left(g\left(x\right)\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

27.

If $f\left(x\right)=x^2$ and $g\left(x\right)=\sqrt{x}$ find $g\left(f\left(x\right)\right)$

a)

$x^4$

b)

$x$

c)

$\sqrt[]{x}$

d)

$x^2$

28.

If $f\left(x\right)=x^2$ and $g\left(x\right)=\frac{1}{x^2}$ find $\left(f\circ g\right)\left(-1\right)$

a)

$\frac{1}{4}$

b)

$1$

c)

$-1$

d)

$-\frac{1}{4}$

29.

When $f(x)=x^2+9$ and $g(x)=x-9$ , find $f(x)-g(x)$

a)

$x^2+x+9$

b)

$x^2-x+9$

c)

$x^2-x$

d)

$x^2-x+18$

30.

When $f(x)=9-3x$ and $g(x)=5x-7$ , find $f(x)+g(x)$

a)

$14x-10$

b)

$-8x+2$

c)

$2x+2$

d)

$2x-2$

31.

If $g\left(x\right)=x^2+6$ and $f\left(x\right)=2x-4$ , find $f\left(g\left(x\right)\right)$

a)

$2x^2-12x-4$

b)

$2x^2+12x-4$

c)

$2x^2+8$

d)

$x^3-2x^2+1$

32.

a)

7

b)

6

c)

11

d)

None of the Above

33.

$g\left(f\left(2\right)\right)$

a)

5

b)

3

c)

-1

d)

2

34.

If $f\left(x\right)=2x+3$ and $g\left(x\right)=-3x-4$ , find $f\left(x\right)\cdot g\left(x\right)$

a)

$-6x^2-17x-12$

b)

$6x^2+x-12$

c)

$-x-1$

d)

$5x+7$

35.

$If\ f\left(x\right)=x^2+3x+2\ \ and\ \ g\left(x\right)=-3x+1$
Find $\left(f+g\right)\left(-2\right)$

a)

-3

b)

3

c)

-7

d)

7

36.

$If\ f\left(x\right)=x^2+3x+2\ \ and\ \ g\left(x\right)=-3x+1$
Find $\left(f\cdot g\right)\left(1\right)$

a)

-2

b)

2

c)

-12

d)

12

37.

$If\ f\left(x\right)=x^2+3x+2\ \ and\ \ g\left(x\right)=-3x+1$
$Find\ \left(\frac{f}{g}\right)\left(0\right)$

a)

-2

b)

-1

c)

0

d)

2

38.

$If\ f\left(x\right)=3x^2-2x+1\$

Find\ f\left(4\right)+f\left(-2\right)

a)

-52

b)

-7

c)

58

d)

63

39.

$If\ f\left(x\right)=2x+1\ \ and\ \ g\left(x\right)=3x+2$

Find\ \left(f\circ g\right)\left(x\right)

a)

f(g(x)) = 6x + 4

b)

f(g(x)) = 6x + 5

c)

f(g(x)) = 5x + 8

d)

f(g(x)) = 5x + 5

40.

$If\ f\left(x\right)=x^2-5\ \ and\ \ g\left(x\right)=2x-3$

Find\ \left(g\circ f\right)\left(2\right)

a)

-5

b)

-3

c)

0

d)

2

41.

$If\ f\left(x\right)=2x^2+3\ \ and\ \ g\left(x\right)=2x-1$
$Find\ \left(g\circ f\right)\left(2\right)$

a)

$g\left(f\left(2\right)\right)=-5$

b)

$g\left(f\left(2\right)\right)=0$

c)

$g\left(f\left(2\right)\right)=20$

d)

$g\left(f\left(2\right)\right)=21$

42.

$If\ f\left(x\right)=2x^2+3\ \ and\ \ g\left(x\right)=2x-1$

Find\ \left(f\circ g\right)\left(-3\right)

a)

$f\left(g\left(-3\right)\right)=83$

b)

$f\left(g\left(-3\right)\right)=89$

c)

$f\left(g\left(-3\right)\right)=99$

d)

$f\left(g\left(-3\right)\right)=101$

MC 8.3 Function Operation and Composition

Total questions: 42

Worksheet time: 2hrs 37mins

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