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

1. hba

Show me what ya got :)

2. Loujoelou

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 $\pm 9 \sqrt{x} = y$

3. hartnn

how u got y- 9 ??

4. hba

Interesting :)

5. hartnn

but incorrect :P

6. Loujoelou

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

7. hartnn

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...

8. Loujoelou

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

9. hba

@hartnn Bache mai halka haat rakho :)

10. hartnn

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.

11. Loujoelou

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

12. hartnn

welcome ^_^