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## korosh23 one year ago What is the inverse of the function f(x) = (x+2) ^2 ???

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1. korosh23

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

2. korosh23

Am I right?

3. Astrophysics

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)

4. Astrophysics

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

5. Astrophysics

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

6. Astrophysics

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

7. Astrophysics

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

8. korosh23

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

9. rajat97

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:$y=\sqrt{x} -2$

10. korosh23

ok I got it thank you

11. rajat97

you're welcome

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