Free Printable Skill check M1-M3

1.

Let

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

2.

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

3.

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

4.

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

5.

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

6.

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

7.

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

8.

a)

Inverse Functions

b)

Not Inverse Functions

9.

Are the following inverses of each other?

a)

True

b)

False

10.

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

a)

(1, 4) and (4, 6)

b)

(-4, -1) and (-6, -4)

c)

(-1, -4) and (-4, -6)

d)

(4, 1) and (6, 4)

11.

Find the correct order to find the inverse of f(x)= 2x-5

a)

y=2x-5

b)

2y-5=x

c)

2y= x+5

d)

$y=\frac{x+5}{2}$

e)

$f^{-1}\left(x\right)=\frac{1}{2}x+\frac{5}{2}$

1)

2)

3)

4)

5)

12.

a)

A

b)

B

c)

C

d)

D

13.

Are these functions inverses?

a)

Yes

b)

No

14.

Are these inverse functions?

a)

no

b)

yes

c)

no way to tell

15.

Which graph shows the inverse of the graph above?

a)

b)

c)

d)

16.

Which graph shows inverse functions?

a)

b)

c)

d)

17.

What is the inverse of the points
(1,3)(2,4)(6,8)

a)

(3,1)(4,2)(8,6)

b)

(-3,-1)(-4,-2)(-8,-6)

c)

(1,3)(2,4)(6,8)

d)

(-1,-3)(-2,-4)(-6,-8)

18.

What is the RANGE of the INVERSE function?

a)

{-5, 1, 3, 4}

b)

{-4, -3, -1, 5}

c)

{-4, -2, 0, 7}

d)

{-7, 0, 2, 4}

19.

Which of the following is NOT TRUE about inverse functions?

a)

Inverse functions are reflections of each other over the line y = x.

b)

You find the inverse by switching x and y in the equation.

c)

The domain of a function becomes the domain of its inverse.

d)

The domain of a function becomes the range of its inverse.

20.

If f^-1(-25) = 7 then what is f(7) =

21.

Determine the inverse for the function:

R (x) = 2x + 1

(Write your answer as y = ... )

22.

Determine the inverse for the function:

T(x) = $6x\ -\ 7$

(Write your answer as y = ... )

23.

Which is the inverse of the table?

a)

b)

c)

d)

24.

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

25.

h(f(-2)) =

26.

f(f(0)) =

27.

If $f\left(x\right)=x^2-2,$ $g\left(x\right)=x+9$ and $h\left(x\right)=-3x,$ find $h\left[f\left(g\left(-2\right)\right)\right].$

28.

If $f\left(x\right)=\frac{6}{7}x+3,$ $g\left(x\right)=\frac{2}{3}x-1$ and $h\left(x\right)=\frac{1}{4}x+6,$ find $f\left[g\left(h\left(24\right)\right)\right].$

29.

p(x) = 3x + 4
q(x) = 2x²
Find p(q(x))

30.

Evaluate the function $f\left(x\right)=x^2+4x+1$ when $x=-2$ .

31.

$f\left(x\right)=\sqrt{x-6}$ , find $f\left(15\right)$

32.

If $f\left(x\right)=\frac{2x\ +1}{x-1}$

find $f\left(\frac{3}{2}\right)$

33.

State the domain

a)

(-oo, -1) U (-1, oo)

b)

[-1, oo)

c)

(-oo, -1]

d)

(-1, oo)

34.

State the domain:

a)

(-oo, 7) U (7, oo)

b)

(-oo, -7) U (7, oo)

c)

(7, oo)

d)

[7, oo)

35.

State the domain:

a)

(-oo, 4)

b)

(-oo, 2]

c)

[2, oo)

d)

[4, oo)

36.

State the domain

a)

(-oo, oo)

b)

[0, oo)

c)

(-oo, 0]

d)

(-oo, 0) U (0, oo)

37.

State the domain:

a)

(-oo, oo)

b)

(-oo, 3) U (3, oo)

c)

(-oo, -3) U (-3, 3) U (3, oo)

d)

[3, oo)

38.

State the domain:

a)

(-oo, 2]

b)

[5, oo)

c)

(-oo, 5/2]

d)

[5/2, oo)

39.

State the domain:

a)

(-oo, 3) U (3, oo)

b)

(-oo, 3]

c)

(-oo, 3)

d)

(3, oo)

40.

State the domain:

a)

(-oo, oo)

b)

[0, oo)

c)

(-oo, 0)

d)

(0, oo)

41.

$g\left(x\right)=\frac{x+5}{x-1}$ Find the x-values where g(x)=0

a)

x = 1

b)

x = -1

c)

x = -5

d)

x = 5

42.

Find $h(f(j(19)))$

43.

Given that $f\left(x\right)=x^{ }+1$ and $g\left(x\right)=\frac{1}{x+3}$ Find the domain of the division $\frac{g\left(x\right)}{f\left(x\right)}$

a)

(-∞,-3) ∪ (-3, -1) ∪

(-1, ∞)

b)

(-∞,-3) ∪ (-3, ∞)

c)

(-∞,-1) ∪ (-1, ∞)

d)

(-3,-1)

44.

Given that $f\left(x\right)=x^2-1$ and $g\left(x\right)=\frac{1}{x+3}$ Find the domain of the division $\frac{g\left(x\right)}{f\left(x\right)}$

a)

(-∞,-3) ∪ (-3, -1) ∪

(-1, ∞)

b)

(-∞,-3) ∪ (-3, -1) ∪

(-1, 1) ∪ (1, ∞)

c)

(-∞,-1) ∪ (-1, ∞)

d)

(-∞,-3) ∪ (-3, 1) ∪

(1, ∞)

Skill check M1-M3

Total questions: 44

Worksheet time: 1hrs 24mins

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