Let f(x) = x^2 – 81. Find f–1(x).
Can someone double-check what I have?

Question

Let f(x) = x^2 – 81. Find f–1(x). 
Can someone double-check what I have?

hba · Answer

Show me what ya got :)

anonymous · Answer

Okay so I know first to substitute f(x) with y and then to reverse the x & y variables which would give me x=y^2-81. Then I use a root on both sides and get $$\pm x=y-9$$ and finally I add 9 on both sides to get $$\pm 9 \sqrt{x}   = y$$

hartnn · Answer

how u got y- 9 ??

hba · Answer

Interesting :)

hartnn · Answer

but incorrect :P

anonymous · Answer

well we have y^2-81, idk factoring it would be (y+9)(y-9) but am I supposed to do that?

hartnn · Answer

no, what you did was $\sqrt{y^2-81}=y-9$
that is incorrect. 
whats to be done : 
let y= x^2-81
add 81 to both sides.
then take square root of both sides...

anonymous · Answer

oh okay :) so it'd be x+81= y^2 and once we square root both sides would the answer come out to $$\pm 9 \sqrt{x}=y$$

hba · Answer

@hartnn 

Bache mai halka haat rakho :)

hartnn · Answer

taking square root on both sides of $x+81=y^2$
will give you 
$\sqrt{x+81}=\sqrt{y^2}=y$
 to get the inverse function as 
$\sqrt{x+81}$
got this ?
hba, i didn't get you.

anonymous · Answer

okay I get it :) thx a ton! :)

hartnn · Answer

welcome ^_^