Inverse Functions

Find the Inverse

89

What is the inverse of

f(x)=(2x + 3) /4

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

 

113

What is the inverse of

g(x) = 1/2(x - 6) 

g^-1(x)= 2x + 6

127

The inverse of

g(x) = (8 - 5x) /4

g^-1(x) = (4x - 8) /5

151

Given f^-1=-x+7, find f(x)

What is f(x)=-x+7

179

What is the inverse of

f(x) = x^2 + 4

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

Are they really inverses?

89

f(x) = (x- 5)/10

h(x) = 10x + 5

What is Yes

113

f(x) = (5x - 9)/ 2

g(x) = (8 + 9x)/2

What is No

127

f(x) = 2x+2 

 

g(x)=2x-2

No

151

f(x) = x + 10

g(x) = -x - 10

No

179

f(x) = 3(x - 9) 

g(x) = 1/3x + 9

What is Yes

Inverse from a chart

89

Given the table of f(x), g(x), and h(x), find 

g^-1(f^-1(2))

x         -1       2       3       4       5       6

f(x)     ND     -1       0       1       2       3

g(x)      1       3       5      ND    ND     ND

h(x)      5       2       1       0      -1      -2    

What is 3 

113

Given the table of f(x), g(x), and h(x), find 

g^-1(h(3))

x         -1       2       3       4       5       6

f(x)     ND     -1       0       1       2       3

g(x)      1       3       5      ND    ND     ND

h(x)      5       2       1       0      -1      -2    

What is  - 1

127

Given the table of f(x), g(x), and h(x), find 

h^-1(f(g^-1(3)))

x         -1       2       3       4       5       6

f(x)     ND     -1       0       1       2       3

g(x)      1       3       5      ND    ND     ND

h(x)      5       2       1       0      -1      -2  

What is 5

151

Given the table of f(x), g(x), and h(x), find 

g(f^-1(-1))

x         -1       2       3       4       5       6

f(x)     ND     -1       0       1       2       3

g(x)      1       3       5      ND    ND     ND

h(x)      5       2       1       0      -1      -2  

What is 3?

179

Given the table of f(x), g(x), and h(x), find 

h^-1(g^-1(f(6)))

x         -1       2       3       4       5       6

f(x)     ND     -1       0       1       2       3

g(x)      1       3       5      ND    ND     ND

h(x)      5       2       1       0      -1      -2  

What is 2

Random

89

Find 

f(g(x))

g(x)=2x+7 

f(x)=4x

What is 8x+28

113

Find 

g (f(3)) = 

g(x) = x^2 + 4

f(x) = -x + 6

  

What is 13

127

What must f(g(x)) and g(f(x)) equal in order to prove f(x) and g(x) are inverse functions?

x

151

The domain of an invertible function is 7<x<50. What does this tell us about the inverse function?

What is range of 7<y<50?

179

 Find f ^-1(x)

f(x)=(6x+3)/3

What is f ^-1(x)=^x/₂ - ¹/₂ 

Graphs

89

Which function is one-to-one and therefore has an inverse function?

y= x² +3       or      y= ^5x/₃ - ¹/₄

What is y= ^5x/₃ - ¹/₄

113

Will the function and its inverse always intercept?

No if the lines are parallel to the line of reflection 

127

If the function has an y-intercept at -4, what do I know about its inverse graph?

the inverse would have a x-intercept at -4. 

151

What line will the function reflect over to graph the inverse function?

y = x

179

Find the inverse for each relation.

 { (1, -3), (-2, 3), (5, 1), (6, 4) }

What is {(-3,1), (3,-2), (1,5), (4,6)}