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Function Combinations Review

Total questions: 50

Worksheet time: 3hrs 30mins

Name
Class
Date
1.

Find the inverse function.

h(x)=−x−3h\left(x\right)=-x-3  

a)

h−1(x)=−2xh^{-1}\left(x\right)=-2x  

b)

h−1(x)=2x−6h^{-1}\left(x\right)=2x-6  

c)

h−1(x)=x+2h^{-1}\left(x\right)=x+2  

d)

h−1(x)=−x−3h^{-1}\left(x\right)=-x-3  

2.

Find the inverse function.

g(x)=7x+3g\left(x\right)=7x+3  

a)

g−1(x)=−2x−6g^{-1}\left(x\right)=-2x-6  

b)

g−1(x)=2x−3g^{-1}\left(x\right)=2x-3  

c)

g−1(x)=x−37g^{-1}\left(x\right)=\frac{x-3}{7}  

d)

g−1(x)=x+73g^{-1}\left(x\right)=\frac{x+7}{3}  

3.

Find the inverse function.

h(n)=n+52h\left(n\right)=\frac{n+5}{2}  

a)

h−1(n)=−2n+1h^{-1}\left(n\right)=-2n+1  

b)

h−1(n)=2n−5h^{-1}\left(n\right)=2n-5  

c)

h−1(n)=−3n+1h^{-1}\left(n\right)=-3n+1  

d)

h−1(n)=−53nh^{-1}\left(n\right)=-\frac{5}{3}n  

4.

Find the inverse. f(x)=−3x+1f\left(x\right)=-3x+1  

a)

f−1(x)=5x+203f^{-1}\left(x\right)=\frac{5x+20}{3}  

b)

f−1(x)=3x−98f^{-1}\left(x\right)=\frac{3x-9}{8}  

c)

f−1(x)=x−52f^{-1}\left(x\right)=\frac{x-5}{2}  

d)

f−1(x)=−x+13f^{-1}\left(x\right)=\frac{-x+1}{3}  

5.

Find the inverse of  f(x)=10+7xf(x)=10+7x  

a)

f−1(x)=x−710f^{-1}(x)=\frac{x-7}{10}

b)

f−1(x)=x−107f^{-1}(x)=\frac{x-10}{7}

c)

f−1(x)=110+7xf^{-1}(x)=\frac{1}{10+7x}

6.

Find the inverse of  f(x)=4xf(x)=4x  

a)

f−1(x)=x4f^{-1}(x)=\frac{x}{4}

b)

f−1(x)=4f^{-1}(x)=4

c)

f−1(x)=14f^{-1}\left(x\right)=\frac{1}{4}

7.

Find the inverse of  f(x)=x−53f(x)=\frac{x-5}{3}  

a)

f−1(x)=35+xf^{-1}(x)=\frac{3}{5}+x

b)

f−1(x)=3x+5f^{-1}(x)=3x+5

c)

f−1(x)=5x+3f^{-1}(x)=5x+3

8.

Find the inverse of  f(x)=2x+1f(x)=2x+1  

a)

f−1(x)=2xf^{-1}(x)=2x

b)

f−1(x)=x−12f^{-1}(x)=\frac{x-1}{2}

c)

f−1(x)=2f^{-1}(x)=2

9.

Find the inverse of  f(x)=3x+2f(x)=3x+2  

a)

f−1(x)=3x−2f^{-1}(x)=3x-2

b)

f−1(x)=2+3xf^{-1}(x)=2+3x

c)

f−1(x)=x−23f^{-1}(x)=\frac{x-2}{3}

10.

The inverse of the function f(x) is written as ...

a)

f -1(x)

b)

f 2(x)

c)

f '(x)

d)

f +(x)

11.
What does it mean to find the inverse of a function?
a)
the x's and y's are switched
b)
the x's and y's are divided by 2
c)
the x's and y's are made negative
d)
the x's and y's are the same
12.

When using composition to verify 2 functions are inverses, g(f(x)) and f(g(x)) must equal

a)

x

b)

y

c)

f(x)

d)

g(x)

13.

Given that f(x) = 3x + 5 and g(x) = 1/3x + 5, Are the two functions inverses of each other?

a)

Yes they are inverses

b)

No, they are not inverses

14.

Are the following inverses of each other? Yes or No

a)

Yes

b)

No

15.

Find the inverse of f(x)=−5x−7f\left(x\right)=-5x-7  

a)

f−1(x)=5x+7−7f^{-1}\left(x\right)=\frac{5x+7}{-7}  

b)

f−1(x)=x+57f^{-1}\left(x\right)=\frac{x+5}{7}  

c)

f−1(x)=x+7−5f^{-1}\left(x\right)=\frac{x+7}{-5}  

d)

f−1(x)=7−5+xf^{-1}\left(x\right)=\frac{7}{-5+x}  

16.

Find the inverse of f(x)=12x−3f\left(x\right)=12x-3  

a)

f−1(x)=x+312f^{-1}\left(x\right)=\frac{x+3}{12}  

b)

f−1(x)=x−312f^{-1}\left(x\right)=\frac{x-3}{12}  

c)

f−1(x)=x+123f^{-1}\left(x\right)=\frac{x+12}{3}  

d)

f−1(x)=x−123f^{-1}\left(x\right)=\frac{x-12}{3}  

17.

Find the inverse of f(x)=12x+8f\left(x\right)=\frac{1}{2}x+8  

a)

f−1(x)=2x+8f^{-1}\left(x\right)=2x+8  

b)

f−1(x)=2x−16f^{-1}\left(x\right)=2x-16  

c)

f−1(x)=2(x+8)f^{-1}\left(x\right)=2\left(x+8\right)  

d)

f−1(x)=12x−16f^{-1}\left(x\right)=\frac{1}{2}x-16  

18.

Find the inverse of f(x)=x2−4f\left(x\right)=x^2-4  

a)

f−1(x)=x+16f^{-1}\left(x\right)=\sqrt{x+16}  

b)

f−1(x)=x−4f^{-1}\left(x\right)=\sqrt{x-4}  

c)

f−1(x)=x+4f^{-1}\left(x\right)=\sqrt{x}+4  

d)

f−1(x)=x+4f^{-1}\left(x\right)=\sqrt{x+4}  

19.

Find the inverse of f(x)=(x−6)2f\left(x\right)=\left(x-6\right)^2  

a)

f−1(x)=x+6f^{-1}\left(x\right)=\sqrt{x}+6  

b)

f−1(x)=x+6f^{-1}\left(x\right)=\sqrt{x+6}  

c)

f−1(x)=x−6f^{-1}\left(x\right)=\sqrt{x}-6  

d)

f−1(x)=x−6f^{-1}\left(x\right)=\sqrt{x-6}  

20.

Find the inverse of f(x)=x−2f\left(x\right)=\sqrt{x-2}  

a)

f−1(x)=x2−2f^{-1}\left(x\right)=x^2-2  

b)

f−1(x)=x2+2f^{-1}\left(x\right)=x^2+2  

c)

f−1(x)=(x+2)2f^{-1}\left(x\right)=\left(x+2\right)^2  

d)

f−1(x)=(x−2)2f^{-1}\left(x\right)=\left(x-2\right)^2  

21.

Find the inverse of f(x)=x+8f\left(x\right)=\sqrt{x}+8  

a)

f−1(x)=x2+8f^{-1}\left(x\right)=x^2+8  

b)

f−1(x)=x2−8f^{-1}\left(x\right)=x^2-8  

c)

f−1(x)=(x+8)2f^{-1}\left(x\right)=\left(x+8\right)^2  

d)

f−1(x)=(x−8)2f^{-1}\left(x\right)=\left(x-8\right)^2  

22.
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
23.
f(x) = 3x2 + 7x and g(x) = 2x2 - x - 1, find (f - g)(x).
a)
x2 + 8x + 1
b)
x2 + 6x - 1
c)
5x2 + 8x - 1
d)
x2 + 8x -1
24.

Find the domain of g(x)=2x−4g\left(x\right)=\sqrt{2x-4}  

a)

(−∞,2)(2,∞)\left(-\infty,2\right)\left(2,\infty\right)  

b)

[2,∞)\left[2,\infty\right)  

c)

(−∞,2]\left(-\infty,2\right]  

d)

(−∞,12)(12,∞)\left(-\infty,\frac{1}{2}\right)\left(\frac{1}{2},\infty\right)  

25.

 Find the domain of y=x2+3x+9y=x^2+3x+9  

a)

(−∞,3)U(3,∞)\left(-\infty,3\right)U\left(3,\infty\right)  

b)

(−∞,3]U[3,∞)\left(-\infty,3\right]U\left[3,\infty\right)  

c)

(−∞,∞)\left(-\infty,\infty\right)  

26.
f(x) = 9-3x
g(x) = 5x-7
Find f(x)+g(x). 
a)
14x-10
b)
-8x+2
c)
2x+2
d)
2x-2
27.
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
28.
Which one of the following functions is even?
a)
f(x) = x⁴ + x³
b)
g(x) = x⁴ + x²
c)
h(x) = x⁵ + x³
d)
k(x) = x³ + x
29.
Which one of the following functions is odd?
a)
f(x) = 3x⁴ - 4x³
b)
g(x) = 5x⁴ + 3x²
c)
h(x) = 6x⁵ - x³
d)
k(x) = x⁶ + 8x²
30.

Is the function even, odd, or neither?

f(x) = x2 + 2

a)

Even

b)

Odd

c)

Neither

31.

y=8x12−8x4+6x+22y=8x^{12}-8x^4+6x+22  

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

32.
Is the function even, odd, or neither?
 f(x)=5
a)
even
b)
odd
c)
neither
33.

Is the polynomial function even, odd, or neither? (Hint: Use f(-x) )

f(x) = 5x4 - 4x2 + 3

a)

odd

b)

neither

c)

even

34.

Is this function even, odd, or neither?

a)

even

b)

odd

c)

neither

35.

Find the difference of the given functions: f(x)=7x3−3x2+4x−6f\left(x\right)=7x^3-3x^2+4x-6  and  g(x)=6x3−8x2−5x−7g\left(x\right)=6x^3-8x^2-5x-7  

a)

(f−g)(x)=x3+5x2+9x+1\left(f-g\right)\left(x\right)=x^3+5x^2+9x+1  

b)

(f−g)(x)=x3+5x2+9x−1\left(f-g\right)\left(x\right)=x^3+5x^2+9x-1  

c)

(f+g)(x)=x3+5x2+9x+1\left(f+g\right)\left(x\right)=x^3+5x^2+9x+1  

36.

Given f(x) = 3x2 + 7x and g(x) = 2x2 - x - 1, find (f + g)(x). #4

a)
11x2 - 1
b)
5x4 + 6x2 - 1
c)
5x2 + 6x - 1
d)
5x2 + 8x - 1
37.

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

a)
x2 + 8x + 1
b)
x2 + 6x - 1
c)
5x2 + 8x - 1
d)
x2 + 8x -1
38.

Which expression is equivalent to

(10+7r−r2)+(−6r2−18+5r)?\left(10+7r-r^2\right)+\left(-6r^2-18+5r\right)?  

a)

−7r2+2r+8-7r^2+2r+8  

b)

7r2+12r+87r^2+12r+8  

c)

−7r2+12r−8-7r^2+12r-8  

d)

7r2+2r−87r^2+2r-8  

39.

g(n) = n2 + 5n

f(n) = n + 4

Find (g o f)(n)

a)

n2 + 3n + 36

b)

n2 + 13n + 16

c)

n2 + 13n + 36

d)

n2 + 3n + 20

40.

If f(x) = 3x-1 and g(x) = x2+2,

what is (f ° g)(x) ?

a)

3x2 +5

b)

x2 +1

c)

3x2 +1

d)

3x2 +6

41.
g(x)=3x+4
h(x)=3x-1
Find (g∘h)(x)
a)
-9x+11
b)
4x2+4x
c)
9x+1
d)
9x+11
42.

If f(x) = x-5 and g(x) = 3x2-1,

what is (f ° g)(x) ?

a)

3x2-5

b)

3x2-1

c)

3x2-4

d)

3x2-6

43.
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
44.
f(x) = 9-3x
g(x) = 5x-7
Find f(x)+g(x). 
a)
14x-10
b)
-8x+2
c)
2x+2
d)
2x-2
45.
f(x)=x2+1
g(x)=2x-5
Find f(x)-g(x)
a)
x2-2x+6
b)
-x2+2x+4
c)
-x2-2x-6
d)
x2-2x-4
46.
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
47.
f(x)=x3-3x
g(x)=-4x+1
Find f(x)*g(x)
a)
-4x3-5x2-3
b)
-4x3+2x2-3x
c)
-4x4+x3+12x2-3x
d)
-4x4-x3+12x2+3x
48.
f(x)=2x+4
g(x)=3x2-1
Find f(x)*g(x)
a)
6x4+12x3-4x2-8x
b)
-6x3+12x2+2x-4
c)
6x3+12x2-2x-4
d)
5x2-18x+20
49.
f(n)=2n+1
g(n)=3n
Find f(n)+g(n)
a)
5n+1
b)
-5n+1
c)
-2n+1
d)
-6n-1
50.
f(n)=n2+4n
g(n)=-n-5
Find f(n)+g(n)
a)
n2+3n-5
b)
-n3+2n-7
c)
n3+3n-3n
d)
n2-3n-5

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