the function f(x)=8x/8x+5 is one to one. find its inverse f^-1(x)

Question

anonymous · Answer

yikes
you gotta solve 
$$x=\frac{8y}{8y+5}$$ for $y$ 
any ideas ?

anonymous · Answer

i can walk you through it if you like

anonymous · Answer

yes please

anonymous · Answer

ok 
but maybe first we solve 
$$\frac{8y}{8y+5}=7$$ so we can understand what is going on

anonymous · Answer

$$8y=7(8y+5)\
8y=56y+35\
-48y=35\
y=-\frac{35}{48}$$

anonymous · Answer

use the same steps, only without numbers, just variables $x$ and $y$

anonymous · Answer

$$x=\frac{8y}{8y+5}$$ multiply both sides by $8y+5$ get 
$$x(8y+5)=8y$$ multiply out on the left get 
$$8xy+5x=8y$$ add $5x$ to both sides and subtract $8y$ get 
$$8xy-8y=-5x$$ factor out the $y$ 
$$(8x-8)y=-5x$$ divide 
$$y=\frac{-5x}{8x-8}$$

anonymous · Answer

i said something wrong, should be "subtract $5x$ from both  sides" but the answer is right i think

anonymous · Answer

wanna check it?

mosaic · Answer

Another way to do this is to take the reciprocal as the first step: 1/x = 1 + 5/8y

anonymous · Answer

yeah i guess what would work too in this case, since the numerator has only one term

anonymous · Answer

@babijenny  you ok with this?