Question

The graph of a function g is shown below.

Answer 1

Answer:

$g^{-1}(x)=2.5x+5$

Step-by-step explanation:

step 1

Find the equation of the function g(x)

Let

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

Find the slope m

$m=(0+2)/(5-0)\\m=2/5$

Find the equation of the line into slope intercept form

$g(x)=mx+b$

we have

$m=2/5\\b=-2$

substitute

$g(x)=(2/5)x-2$

step 2

Find the inverse of g(x)

Let

y=g(x)

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

Exchange the variables, x for y and y for x

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

Isolate the variable y

Multiply by 5 both sides to remove the fraction

$5x=2y-10$

$2y=5x+10$

$y=2.5x+5$

Let

$g^{-1}(x)=y$

so

$g^{-1}(x)=2.5x+5$