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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

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 class=

Answer :

calculista

Answer:

[tex]g^{-1}(x)=2.5x+5[/tex]

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

[tex]m=(0+2)/(5-0)\\m=2/5[/tex]

Find the equation of the line into slope intercept form

[tex]g(x)=mx+b[/tex]

we have

[tex]m=2/5\\b=-2[/tex]

substitute

[tex]g(x)=(2/5)x-2[/tex]

step 2

Find the inverse of g(x)

Let

y=g(x)

[tex]y=(2/5)x-2[/tex]

Exchange the variables, x for y and y for x

[tex]x=(2/5)y-2[/tex]

Isolate the variable y

Multiply by 5 both sides to remove the fraction

[tex]5x=2y-10[/tex]

[tex]2y=5x+10[/tex]

[tex]y=2.5x+5[/tex]

Let

[tex]g^{-1}(x)=y[/tex]

so

[tex]g^{-1}(x)=2.5x+5[/tex]

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