# inverse of function

Thanks for the help! Here is the solution..

i had a problem: $$f(x)=\frac{(\sqrt x+8)}{(5-\sqrt x)}$$

i had to find the inverse, so lets begin...

1) first i write in terms of $y$

$$y=\frac{(\sqrt x+8)}{(5-\sqrt x)}$$

2) now try to get $x$ by itself

$$(5-\sqrt x)y=\sqrt x+8$$

3)Distribute y along the left hand side both sides

$$(5y-y\sqrt x)=\sqrt x+8$$

4)subtract 8 and from both sides and add $$y\sqrt x$$ to both sides

$$5y-8=y\sqrt{x} + \sqrt x$$

5) factor right hand side

$$5y-8=\sqrt{x} (y + 1)$$

6)divide out $$(y+1)$$ from right side

$$((5y-8)/(y+1))=\sqrt x$$

7) square both sides leaving $$x=((5y-8)/(y+1))^2$$

8) so the solution is $$f^-1(x)=((5x-8)/(x+1))^2$$

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please type the equations in \$\$. thx- – Seyhmus Güngören Feb 12 '13 at 0:28
Step 3) is invalid. You should distribute $y$ across the sum in the left hand side first. Then collect all terms containing "$\sqrt x$" on one side, and factor it out. – David Mitra Feb 12 '13 at 0:29
Ditto for step 4). – Gerry Myerson Feb 12 '13 at 0:32

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