Question

Inverse of the function h(x)=\dfrac{3}{2}(x-11)h(x)= 2 3 ​ (x−11)h, left parenthesis, x, right parenthesis, equals, start fraction, 3, divided by, 2, end fraction, left parenthesis, x, minus, 11, right parenthesis?

Answer 1

`h^(-1)(x)=(2)/(3)x+11`

Explanation:

The given function is

`h(x)=(3)/(2)(x-11)`

We need to find the inverse of the given function.

Step 1: Substitute h(x)=y.

`y=(3)/(2)(x-11)`

Step 2: Interchange x and y.

`x=(3)/(2)(y-11)`

Step 3: Isolate y.

`(2)/(3)x=y-11`

`(2)/(3)x+11=y`

Step 4: Interchange sides.

`y=(2)/(3)x+11`

Step 5: Substitute
`y=h^(-1)(x)`.

`h^(-1)(x)=(2)/(3)x+11`

Therefore, the inverse of the function is
`h^(-1)(x)=(2)/(3)x+11`.