Inverse Functions

When finding the inverse of a relation,

1st: replace f(x) with y 2nd: switch the x's and y's

What do you do next?

• solve for y
• replace y with f^-1(x)
• solve for x
• find the greatest common factor

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

• f ^-1(x)
• f ²(x)
• f '(x)
• f ⁺(x)

F(x) = x + 11

Then use 4 step to find inverse F^-1(x)

• S1: let F(x) = x + 11

  S2: Interchange x <=> y

  x = y + 11

  S3: Solve for y

  11x = y

  S4: F(x)^-1 = 11x

• S1: let y = x + 11

  S2: Interchange x <=> y

  y + 11 = x

  S3: Solve for y

  y = x + 11

  S4: F(x)^-1 = x + 11

• S1: let y = x + 11

  S2: Interchange x <=> y

  x = y + 11

  S3: Solve for y

  x - 11 = y

  S4: F(x) = x

• S1: let y = x + 11

  S2: Interchange x <=> y

  x = y + 11

  S3: Solve for y

  x - 11 = y

  S4: F^-1(x) = x - 11

f(x) = -4x - 12

What is f^-1(x)?

• f^-1(x) = 4x - 3

• f^-1(x) = -1/4x - 3

• f^-1(x) = 1/4x + 3

• f^-1(x) = -4x - 3

Which is f ^-1(x)?

• f ^-1(x) = 3x + 5

• f ^-1(x) = 3x - 5

• f ^-1(x) = 3x - 15

• f ^-1(x) = 3x + 15

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

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

Find the inverse.

f(x)=2x-2      

• f^-1(x)=1/2x+1
• f^-1(x)=-2-1/2x
• f^-1(x)=-7/3x-20/3
• 2-2/5x

What does it mean to find the inverse of a function?

• switch the x's and y's

• divide the x's and y's by 2

• make the x's and y's negative

• make the x's and y's the same