Question

Find the inverse function of h(x) = -2/3x + 6.

Answer 1

`x=-(3)/(2) x+9`

Explanation:

We are given the following function and we are to find the inverse of this function:

`h(x) = - \frac { 2 } { 3 } x + 6`

For that, we will put the function equal to another variable
`y` and make
`x` the subject of the function.

`y = - \frac { 2 } { 3 } x + 6`

Making
`x` the subject:

`y-6=-(2)/(3) x`

`3(y-6)=-2x`

`(3y-18)/(-2) =x`

`x=-(3)/(2) x+9`

Therefore, the inverse h'(x) =
`x=-(3)/(2) x+9`.

Answer 2

`h^(-1)(x)=-(3)/(2)x+9`

Explanation:

To find inverse of a function, follow the steps below:

1. replace h(x) with y

2. Interchange x and y

3. Solve for the new y

4. Replace y to
`h^(-1)(x)` (this is the inverse function)

Step 1: y = -2/3x+6

Step 2: x = -2/3y+6

Step 3:

`x=-(2)/(3)y+6\\(2)/(3)y=-x+6\\y=(-x)/((2)/(3))+(6)/((2)/(3))\\y=-(3)/(2)x+9`

Step 4:

`y=-(3)/(2)x+9\\h^(-1)(x)=-(3)/(2)x+9`

This is the inverse function.