Question

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

Answer 1

I believe the answer is:

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

Answer 2

Am I right?

Answer 3

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)

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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:\[y=\sqrt{x} -2\]

Answer 10

ok I got it thank you

Answer 11

you're welcome