Question

A function is defined by the equation y=x−2x+5. Which equation defines the inverse of this function?

Answer 1

Finding the Inverse of a Function:

1. First, replace f(x) with y .

1. First, replace f(x) with y . 2. Replace every x with a y and replace every y with an x .

1. First, replace f(x) with y . 2. Replace every x with a y and replace every y with an x .3. Solve the equation from Step 2 for y .

1. First, replace f(x) with y . 2. Replace every x with a y and replace every y with an x .3. Solve the equation from Step 2 for y . 4. Replace y with f−1(x) f − 1 ( x ) .

1. First, replace f(x) with y . 2. Replace every x with a y and replace every y with an x .3. Solve the equation from Step 2 for y . 4. Replace y with f−1(x) f − 1 ( x ) .5. Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.

____ INFORMATION BY ARYAN