Given the function f(x)=(x-9)^2 where x is less than or equal to 9 , find f^-1(x) and its domain.

The domain of is .

Question

Given the function f(x)=(x-9)^2 where x is less than or equal to 9 ,  find f^-1(x) and its domain.

The domain of  is .

turingtest · Answer

y=(x-9)^2
$$\sqrt{y}=x-9$$$$x=\sqrt{y}+9$$so the inverse of f(x) is$$f^{-1}(x)=\sqrt{x}-9$$
The domain is the set of all x for which f(x) is defined. We are told that $$x \le 9$$ and if $$x<0$$ the radical gives an imaginary number, so the range is$$0<x \le 9$$ or in interval notation:$$(0,9]$$

turingtest · Answer

sorry, I meant the DOMAIN is
$$0\le x \le 9$$ or $$[0,9]$$

turingtest · Answer

x=0 is okay since it doesn't yield an undefined or imaginary number, so I used closed brackets.

anonymous · Answer

i tried this, but its all wrong according to my online thing :(

turingtest · Answer

you got the same answer as me?

anonymous · Answer

i got sqrt(x)+9 but i typed yours in and both were wrong as well as the interval notation

turingtest · Answer

yeah my bad, should be sqrt(x)+9 but that doesn't change the answer: [0,9]
if your online thing says this interval is wrong I am suspicious of it. Still, don't give me a medal (so your post still says "needs a good answer") and see if anyone else comes up with something different. I can't see how my answer is wrong.

anonymous · Answer

thanks

anonymous · Answer

i have another question on the newfeed if u could please help thanks for ur time