Given the function f(x)=(x-12)^2 where x less than or equal to 12 , find f-1(x) and its domain.

Question

Given the function f(x)=(x-12)^2  where x less than or equal to 12 ,  find f-1(x)  and its domain.

anonymous · Answer

sqrt(y) = x - 12
x = sqrt(y) + 12

anonymous · Answer

so inverse is
y = sqrt(x) + 12

anonymous · Answer

it's domain will be x >= 0

anonymous · Answer

thank you

anonymous · Answer

wait so does that mean [0,inf)

anonymous · Answer

yup

anonymous · Answer

domain is right. web work keeps saying the answer, the inverse function that is, is wrong

tkhunny · Answer

It's always good to find the Domain and Range of $f(x)$ before you start.  This makes the Range and Domain of $f^{-1}(x)$ rather trivial.

Anyway, let's try that swap-and-solve again.

If $y = (x-12)^{2}$

We have $x = (y-12)^{2}$ to solve for $y$

The square root - be very carful, here

$\pm\sqrt{x} = y-12$

Finally, $y = 12 \pm \sqrt{x}$

Notice how there are TWO answers.  The challenge of this problem is to pick the correct branch.

Hint:  Whe had the Domain and Range of $f(x)$.  Which branch reflects those original properties?