Question

Find the inverse of f(x) = -2x+5

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

Answer 1

Given:

The function is:

`f(x)=-2x+5`

To find:

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

Solution:

We have,

`f(x)=-2x+5`

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

`y=-2x+5`

Step 2: Interchange x and y.

`x=-2y+5`

Step 3: Isolate variable y.

`2y=5-x`

`y=(5-x)/(2)`

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

`f^(-1)(x)=(5-x)/(2)`

Therefore, the inverse of the given function is
`f^(-1)(x)=(5-x)/(2)` and the graphs of these functions are shown below.

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