Question

Find f-1(x) if f(x) = 2x/3-4

Answer 1

Given:

The function is:

`f(x)=(2x)/(3)-4`

To find:

The inverse of the given function, i.e.,
`f^(-1)(x)`.

Solution:

We have,

`f(x)=(2x)/(3)-4`

Step 1: Substitute
`f(x)=y`.

`y=(2x)/(3)-4`

Step 2: Interchange x and y.

`x=(2y)/(3)-4`

Step 3: Isolate y.

`x+4=(2y)/(3)`

`3(x+4)=2y`

`(3x+12)/(2)=y`

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

Step 4: Substitute
`y=f^(-1)(x)`.

`f^(-1)(x)=(3)/(2)x+6`

Therefore, the inverse of the given function is
`f^(-1)(x)=(3)/(2)x+6`.