Inverse Functions with Jay + Practice Problems!

What is an inverse function? 

• An inverse function is a function that "undoes" what another function did to an input. 

For example, if you plugged in the value of 4 into function B and got 10, and plugged in 10 into the inverse of function B, you should get 4 back out of the inverse function. 

How To Find the Inverse of a Function

Step 1: Get the function

Y = x + 4

Step 2: Change the locations of Y and X

X = y + 4

Step 3: manipulate the equation to have y isolated on one side

Y = x - 4

Step 4: Done

Y = x - 4 (Final inverse equation)

Step 5: Check by plugging back in

(plug in 4 for x)

Y = x (4) - 4

Y = 0

(Plug back in 0 to the inverse)

0 = x  - 4

X = 4

(Same as what we plugged in)

These Steps work for any kind of equation, whether its a parabola or linear 

Practice Problems

1. Y = 4 / x + 2

2. Y = (x + 1) / (x + 2)

3. Y = -5x + 1

4. -1 + xˆ3

5. Y = -3x / 4

6. Y = (- x + 2 ) / 3

7. Y = (5x - 5) /4

8. Y = (-2x + 1)/ 3

9. Y = -1 / (x + 1)

10. Y = X / x + 2

Answers

1. (4 - 2x) / x

2. (-2x + 1)/ x + 1

3. (-x + 1) / 5

4. Cube root of (x + 1)

5. -4x / 3

6. -3x + 2

7. (5 + 4x) / 5

8. (-3x + 1) / 2

9. (-1 - x) / x

10. -2x / (x - 1)