What is the inverse of the function f(x) = (x+2) ^2 ???

Question

What is the inverse of the function f(x) = (x+2) ^2    ???

korosh23 · Answer

I believe the answer is:

$$f^-1 (x)= \sqrt{x -2}$$

korosh23 · Answer

Am I right?

astrophysics · Answer

To find the inverse:

Replace f(x) with y
Switch x's and y's, so put x where y is and x where y is.
Solve for y
Replace y with f^-1(x)

astrophysics · Answer

$$y=(x+2)^2 \implies x = (y+2)^2$$ $$y+2=\sqrt{x} \implies y = \sqrt{x}-2$$

astrophysics · Answer

I think you may have made a mistake sqaure rooting both sides

astrophysics · Answer

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

astrophysics · Answer

I guess we should put $$f^{-1}(x) = \pm \sqrt{x}-2$$ if you really want to be precise

korosh23 · Answer

why the square root is not part of the -2 ? @Astrophysics

rajat97 · Answer

look we just need to find x in terms of y 
so we have y=(x+2)^2
so sqrt(y) = x+2
then, sqrt(y) -2 = x
now just interchange x and y
so, you'll get, sqrt(x) - 2 = y
it seems to be like this:$$y=\sqrt{x} -2$$

korosh23 · Answer

ok I got it thank you

rajat97 · Answer

you're welcome