Question

Find the inverse of f(x) = 6x.

The inverse is
g(x) =
Graph the function and its inverse

Answer 1

Given:

The function is:

`f(x)=6x`

To find:

The inverse of the given function, then draw the graphs of function and its inverse.

Solution:

We have,

`f(x)=6x`

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

`y=6x`

Step 2: Interchange x and y.

`x=6y`

Step 3: Isolate variable y.

`(x)/(6)=y`

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

`(x)/(6)=f^(-1)(x)`

Therefore, the inverse of the given function is
`f^(-1)(x)=(x)/(6)` and the graphs of these functions are shown below.

Note: The inverse function is
`g(x)=f^(-1)(x)`.