Question

Find the inverse function of y=(x-2)^2 + 3. please show steps

Answer 1

`f^(-1)(x)=2\pm√(x-3)`

Explanation:

we have

`y=(x-2)^2+3`

step 1

Exchange the variables (x for y and y for x)

so

`x=(y-2)^2+3`

Isolate the variable y

step 2

`x=(y-2)^2+3`

subtract 3 both sides

`(y-2)^2=x-3`

step 3

square root both sides

`y-2=\pm√(x-3)`

step 4

Adds 2 both sides

`y=2\pm√(x-3)`

step 5

Let

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

`f^(-1)(x)=2\pm√(x-3)`