Question

The graph of a function g is shown below. Find its inverse.

Answer 1

the inverse graph should be on the other side of the Y=X line therefore the inverse graph can be found by swapping the X coordinates and Y coordinates so the inverse graph should go through the points (-2,0) and (0,5)

Answer 2

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

Explanation:

step 1

Find the equation of the graph

Let

`A(0,-2), B(5,0)`

The slope of the linear equation is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values

`m=(0+2)/(5-0)`

`m=(2)/(5)`

The equation of the line into point-slope form is equal to

`y-y1=m(x-x1)`

substitute

`y-0=(2)/(5)(x-5)`

`y=(2)/(5)x-2` --------> linear equation of the graph

Step 2

Find the inverse function

Exchanges the variables x for y and y for x

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

Isolate the variable y

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

Let

`f^(-1)(x)=y`

`f^(-1)(x)=(5)/(2)x+5` --------> inverse of the function of the graph