Question

The inverse of y = 2x + 2 is

Answer 1

The inverse of y = 2x+2 is 1/2x-1.

Explanation:

Given equation is

y = 2x+2

let y = f(x) = 2x+2

We have to find the inverse of given function.

Adding -2 to both sides of given equation,we get

y-2 = 2x+2-2

y-2 = 2x

dividing by 2 to both sides of above equation , we have

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

y/2 - 1 = x

Swapping equation, we have

x = y/2-1

put x = f⁻¹(y) in above equation ,we have

f⁻¹(y) = y/2 -1

Replace y with x , we have

f⁻¹(x) = x/2-1

Hence , the inverse of given function is 1/2x-1.

Answer 2

The inverse of given function is
`y=(1)/(2)x-1`.

Explanation:

The given function is

`y=2x+2`

The step and shown below to find the inverse of the function.

Step 1: Interchange x and y.

`x=2y+2`

Step 2: Isolate variable y.

`x-2=2y`

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

`(1)/(2)(x)+(1)/(2)(-2)=y`

`(1)/(2)(x)-1=y`

Therefore the inverse of given function is
`y=(1)/(2)x-1`.