Free Printable 6-2B ALG Verifying Inverses

1.

Q1: If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(f+g\right)\left(x\right)=$

a)

$5x^2+1$

b)

$5x^2-3$

c)

$6x+1$

d)

$6x-3$

2.

Q2: If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(f-g\right)\left(x\right)=$

a)

-4x - 3

b)

-4x +1

c)

6x + 1

d)

6x - 3

3.

Q3: If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(f\cdot g\right)\left(x\right)=$

a)

$5x-3$

b)

$5x^2+2$

c)

$5x^2-7x+2$

d)

$5x-7$

4.

Q4: 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.

Q5: $f(x)=3x+10$

g\left(x\right)=\frac{1}{3}x-3

Find

g(f(x))

a)

$f(g(x))=1$

b)

$f(g(x))=x$

c)

$f(g(x))=0$

d)

None of these.

6.

Q6:

$f\left(x\right)\ =\ -\frac{1}{3}x\ +\ 4\$ and $g\left(x\right)\ -3x\ +12$

what is

f\circ\ g\ \left(6\right)

(a)

7.

Q7:

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

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

(a)

8.

Q8:

(a)

9.

Q9: Which expression represents g(f(x)), if f(x) = 2x - 8

and

g(x) = 4x

a)

8x - 32

b)

8x² - 32x

c)

8x - 8

d)

6x - 8

10.

Q10: 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.

Q11: Which of the following relations is a one-to-one function?

a)

(a)

b)

(b)

c)

(c)

d)

None of these

12.

Q12: The relation in the graph is..

a)

a function, but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

13.

Q13: Was the inverse function found correctly?

a)

no

b)

yes

14.

Q14: Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

15.

Q15: Find the inverse of the function

f(x) = 3x − 5

a)

a. f^-1(x)=3x +5

b)

b. f^-1(x)=(x+5)/3

c)

c. f^-1(x)=3y-5

d)

d. f^-1(x)=3y+5

16.

Q16: Find the inverse of

f(x) = 1/4x - 7

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

17.

Q17: Find the inverse of: $f\left(x\right)=\sqrt{x}-5$

a)

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

b)

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

c)

$f^{-1}\left(x\right)=x^2+25$

d)

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

18.

Q18: To graph the inverse of a function...

a)

Rotate it around the origin

b)

Reflect it across the x-axis

c)

Reflect it across the y-axis

d)

Switch the x and y coordinates and plot the new points

19.

Q19: Graph the inverse

a)

b)

c)

d)

20.

Q20: Are these inverse functions?

a)

yes

b)

no

c)

no way to tell

21.

Q21: To prove two functions are inverses of each other, both f(g(x)) and g(f(x)) should equal...

(a)

22.

Q22: Verify if the two functions are inverses of each other. $f\left(x\right)=-x-5$

$g\left(x\right)=-3x-9$

a)

Inverse Functions

b)

Not Inverse Functions

23.

Q23: $f\left(x\right)\ =\ 5x\ -\ 5$ $g\left(x\right)\ =\ \frac{1}{5}x\ +\ 1$

Use composition of functions to determine if f(x) and g(x) are inverse functions.

a)

yes

b)

no

24.

Q24: Use composition of functions to determine if f(x) and g(x) are inverse functions.

f\left(x\right)=2\sqrt{x}-3

g\left(x\right)=\left(\frac{x+3}{2}\right)^2

a)

yes

b)

no

25.

Q25: Verify if $f\left(x\right)$ and $g\left(x\right)$ are inverses of each other.

$f\left(x\right)=4+\frac{1}{3}x$

g\left(x\right)=3x-12

a)

Inverse Functions

b)

Not Inverse Functions

6-2B ALG Verifying Inverses

Total questions: 25

Worksheet time: 2hrs 37mins

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