Free Printable Assessment: Lesson 5-4 to 5-6

1.

Solve the equation and check for extraneous solutions.
$\sqrt{3x+10}=x+4$

a)

x = -2

b)

x = -2, 3

c)

x = -2, -3

d)

x = -3

2.

Solve the equation and check for extraneous solutions.
$2\sqrt{x}-x=-3$

a)

x = 1

b)

x = 9

c)

x = all real solutions

d)

x = 9, 1

3.

Solve the equation and check for extraneous solutions.
$\sqrt{10-13x}=x-4$

a)

x = 2, 3

b)

x = -2, -3

c)

x = -1, -6

d)

No solution

4.

Solve the equation and check for extraneous solutions.
$\sqrt{\frac{m}{5}}=5$

a)

25

b)

50

c)

125

d)

5

5.

Solve the equation and check for extraneous solutions.
$-6+\sqrt{\frac{k}{6}}=-3$

a)

9

b)

18

c)

486

d)

54

6.

Solve the equation and check for extraneous solutions.
$11=2+\sqrt{90-v}$

a)

9

b)

82

c)

-9

d)

-82

7.

Solve the equation and check for extraneous solutions.
$\sqrt{v-5}=\sqrt{23-v}$

a)

-14

b)

14

c)

no solution

d)

28

8.

Solve the equation and check for extraneous solutions. $10=\sqrt{14r+2}$

a)

102

b)

12

c)

98

d)

7

9.

Solve the equation and check for extraneous solutions. $4=\sqrt{20-x}$

a)

20

b)

-4

c)

4

d)

-10

10.

Solve the equation and check for extraneous solutions. $6+\sqrt{6-15x}=15$

a)

-5

b)

5

c)

10

d)

25

11.

Solve the equation and check for extraneous solutions. $x=\sqrt{4x}$

a)

-4

b)

0, -4

c)

4

d)

0, 4

12.

Solve the equation and check for extraneous solutions. $\sqrt{x}=4$

a)

16

b)

-16

c)

8

d)

4

13.

Solve the equation and check for extraneous solutions. $\sqrt{x}=6$

a)

36

b)

12

c)

6

d)

-36

14.

Solve the equation and check for extraneous solutions. $\sqrt{q+2}=8$

a)

100

b)

66

c)

64

d)

62

15.

Solve the equation and check for extraneous solutions. $\sqrt{2k+1}=19$

a)

180

b)

90

c)

360

d)

-180

16.

Solve the equation and check for extraneous solutions. $\sqrt{q+1}=2$

a)

9

b)

4

c)

3

d)

5

17.

Solve the equation and check for extraneous solutions. $\sqrt{p^2-3p+36}=p+3$

a)

6

b)

3

c)

$-\frac{3}{2}$

d)

-3

18.

Solve the equation and check for extraneous solutions. $\sqrt{12-3x}=\sqrt{x-3}$

a)

No solution

b)

$\frac{15}{4}$

c)

5

d)

15

19.

Solve the equation and check for extraneous solutions. $\sqrt{11-2x}=\sqrt{x-1}$

a)

12

b)

6

c)

4

d)

no solution

20.

Solve the equation and check for extraneous solutions. $\sqrt{x^2+1}=x-7$

a)

no solution

b)

$-\frac{25}{7}$

c)

0

d)

$\frac{24}{7}$

21.

Find (f - g)(x)

a)

5x² + 3x

b)

-3x² - 13x

c)

3x² + 3x

d)

-3x² + 3x

22.

Find (f + g) (x)

a)

5x² + 3x

b)

4x² + 3x

c)

5x² - 3x

d)

4x² - 40x

23.

Find f(2).

a)

-2

b)

-18

c)

24

d)

6

24.

If $f(x)=3x^2+4$ and $g(x)=-2x+2$ ,

find $(g+f)(-3)$ .

a)

39

b)

-27

c)

-23

d)

-19

25.

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

find the domain restriction on $\left(\frac{f}{g}\right)\left(x\right)$ .

a)

$x\ne-1$

b)

$x\ne0$

c)

$x\ne1$

d)

$x\ne\pm1$

26.

If $f(x)=x^2-25$ and $g(x)=x-5$ ,

find the quotient $\left(\frac{f}{g}\right)(0)$ , if it exists.

a)

(f/g)(0) does not exist

b)

10

c)

5

d)

0

27.

Find g(5)

a)

3375

b)

375

c)

25

d)

45

28.

If $f(n)=x^2+1$ and $g(n)=2x-5$ Find $f(n)-g(n)$

a)

$x^2-2x+6$

b)

$-x^2+2x+4$

c)

$-x^2-2x-6$

d)

$x^2-2x-4$

29.

(f + g) (x)

a)

5x² + 3x

b)

4x² + 3x

c)

5x² - 3x

d)

4x² - 40x

30.

If $f(x)=x^2+9$ 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)

$x^2-x+18$

31.

If $f(x)=x^2+5$ and $g(x)=2x^3-1$ ,

find $\left(\frac{f}{g}\right)\left(-3\right)$ .

a)

-14/55

b)

14/55

c)

2

d)

-2

32.

If $f(x)=3x^2+7x$ and $g(x)=2x^2-x-1$ ,

find $(f+g)(x)$ .

a)

$11x^2-1$

b)

$5x^4+6x^2-1$

c)

$5x^2+6x-1$

d)

$5x^2+8x-1$

33.

Given $f\left(x\right)=3x+4$ and $g\left(x\right)=2x+1$ , match the correct rule to its new function.

a)

$6x^2+11x+4$

1.

$\left(f+g\right)\left(x\right)$

b)

$x+3$

2.

$\left(f-g\right)\left(x\right)$

c)

$5x+5$

3.

$\left(f\cdot g\right)\left(x\right)$

d)

$D:\ x\ne-\frac{1}{2}$

4.

$\left(\frac{f}{g}\right)\left(x\right)$

e)

$6x+7$

5.

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

34.

Given $f\left(x\right)=2x^2-9x+2$ and $g\left(x\right)=1-6x$ , what is $\left(f-g\right)\left(x\right)$ ?

35.

Given $g\left(x\right)=1-6x$ and $h\left(x\right)=x^2-4$ , what is $\left(g\cdot h\right)\left(x\right)$ ?

36.

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

37.

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

38.

When f(x) = x²- 9

and g(x) = x + 3 ,

find f(x) / g(x).

a)

$x\ne-3$

b)

$x\ne3$

c)

$x\ne12$

d)

$x\ne-6$

39.

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

40.

Given f(x) = -x + 4 and g(x) = 6x + 3, find (f(x) - g(x))

a)

-7x + 1

b)

5x -1

c)

-5x -1

d)

5x + 1

41.

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

42.

f(x)= 2x+6
g(x)= -3x+2
Find f(x)-g(x)

a)

5x+8

b)

-x+8

c)

x+4

d)

5x+4

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.

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

45.

Perform the indicated operation.

a)

b)

c)

d)

46.

Complete the operation and evaluate.

a)

b)

c)

d)

47.

Evaluate f(2):

f(x)=3x+1

a)

7

b)

9

c)

11

d)

13

48.

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

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

49.

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)

$16x^2-1$

50.

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)

$-\frac{1}{4}$

51.

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

a)

f^-1(x) = 2x + 3

b)

f^-1(x) = -3x + 2

c)

f^-1(x) = (x-2)/3

d)

f^-1(x) = (x-3)/2

52.

Find the inverse

a)

f^-1(x) = 2x+16

b)

f^-1(x) = 2x-16

c)

f^-1(x) = 2x - 8

d)

f^-1(x) = x + 16

53.

a)

A.

b)

B.

c)

C.

d)

D.

54.

When finding the inverse of a relation,
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?

a)

solve for y

b)

replace y with f^-1(x)

c)

solve for x

d)

find the greatest common factor

55.

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

56.

Find the inverse function

a)

b)

c)

d)

57.

Find the inverse function

a)

b)

c)

d)

58.

Find the inverse of $f\left(x\right)=3x+2$

a)

$f^{-1}\left(x\right)=\frac{x-2}{3}$

b)

$f^{-1}\left(x\right)=\frac{x-3}{2}$

c)

$f^{-1}\left(x\right)=\frac{3x}{2}$

d)

$f^{-1}\left(x\right)=\frac{2+x}{3}$

59.

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

a)

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

b)

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

c)

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

d)

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

60.

Find the inverse of $f\left(x\right)=3x+2$

a)

$f^{-1}\left(x\right)=\frac{x-2}{3}$

b)

$f^{-1}\left(x\right)=\frac{x-3}{2}$

c)

$f^{-1}\left(x\right)=\frac{3x}{2}$

d)

$f^{-1}\left(x\right)=\frac{2+x}{3}$

61.

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

a)

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

b)

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

c)

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

d)

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

62.

Find the inverse of $f\left(x\right)=x^2+5$

a)

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

b)

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

c)

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

d)

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

63.

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

a)

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

b)

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

c)

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

d)

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

64.

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

a)

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

b)

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

c)

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

d)

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

65.

Find the inverse of f(x) = 3x +8

a)

f^-1(x) = 3(x-8)

b)

f^-1(x) = (8x-1)/3

c)

f^-1(x) = (x-8)/3

d)

f^-1(x) = (x+8)/3

66.

FInd the inverse of the function.
$f\left(x\right)=\frac{3x-15}{2}$

a)

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

b)

$f^{-1}\left(x\right)=3x+5$

c)

$f^{-1}\left(x\right)=\frac{15+2x}{3}$

d)

$f^{-1}\left(x\right)=\frac{2}{3}x-\frac{19}{3}$

67.

What is the inverse of the function
f(x) = 2x + 4 ?

a)

f^-1(x) = 4(x -2)

b)

f^-1(x) = (x-4)/2

c)

f^-1(x) = x/2 - 4

d)

f^-1(x) = x/4 + 2

68.

What's the name of the inverse of g(x)?

a)

f(x)

b)

f^-1(x)

c)

y

d)

g^-1(x)

69.

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

Assessment: Lesson 5-4 to 5-6

Total questions: 69

Worksheet time: 4hrs 51mins

Similar Resources on Wayground