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

Question

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

anonymous · Answer

lest do it correctly

anonymous · Answer

$$x=(y-9)^2$$
$$y-9=\pm\sqrt{x}$$
$$y=\pm\sqrt{x}+9$$

anonymous · Answer

and now we have to decide plus or minus for the root, because otherwise we do not have a function

anonymous · Answer

okay i got it! thank you so much :)
I have one more problem and I have been working on this for three and a half hours basically. It's my recent one on the newsfeeed. Could you pleaseee help me.

anonymous · Answer

since we choose the domain of f to be 
$$x\leq9$$ we have to choose range of 
$$f^{-1}$$ as 
$$f^{-1}(x)\leq 9$$
$$\pm\sqrt{x}+9\leq 9$$
$$\pm\sqrt{x}\leq 0$$ which means we are picking 
$$-\sqrt{x}$$

anonymous · Answer

okay i got it! thank you so much :)
I have one more problem and I have been working on this for three and a half hours basically. It's my recent one on the newsfeeed. Could you pleaseee help me.

anonymous · Answer

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anonymous · Answer

sure

anonymous · Answer

okay i got it! thank you so much :)
I have one more problem and I have been working on this for three and a half hours basically. It's my recent one on the newsfeeed. Could you pleaseee help me.

anonymous · Answer

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