Question

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

Answer 1

Answer:

$f^{-1}(x)=2\pm\sqrt{x-3}$

Step-by-step 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

$y-2=\pm\sqrt{x-3}$

step 4

Adds 2 both sides

$y=2\pm\sqrt{x-3}$

step 5

Let

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

$f^{-1}(x)=2\pm\sqrt{x-3}$