Question

The graph of a function g is shown below.

Find its inverse.

a. g-1(x) = x + 2
b. g-1(x) = x + 5
c. g-1(x) = x + 5
d. g-1(x) = -x + 2

Answer 1

`g^(-1)(x)=2.5x+5`

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`