someone please help will medal and fan

Question

owlstudies · Answer

$$f(x)=\frac{ x+4 }{ 2x-5 }$$

owlstudies · Answer

find the inverse

satellite73 · Answer

prepared for some algebra ? (a lot of algebra!)?

owlstudies · Answer

oh no. sure.

satellite73 · Answer

i would start by putting $$y=\frac{ x+4 }{ 2x-5 }$$, then switch x and y (because that is what the inverse does) and write $$x=\frac{ y+4 }{ 2y-5 }$$  then solve for $y$

satellite73 · Answer

any idea how to do that?

owlstudies · Answer

nope. no clue

satellite73 · Answer

ok then how about this easier problem $$\frac{y+4}{2y-5}=10$$ can  you solve that?  what is a first step?

owlstudies · Answer

would you multiply both sides by 2y-5?

satellite73 · Answer

yes

owlstudies · Answer

so that would be the first step to solving the one where its equal to x?

satellite73 · Answer

yes, but lets do this one first, so it makes sense

owlstudies · Answer

ok so after you multiply both sides by 2y-5, you would get 20y-50=y+4, then you would subtract y from both sides, add 50 to both sides, and get 54/19

satellite73 · Answer

ok so first step is to multiply by $2y-5$ 
next step was to distribute 
go ahead and do it with the x instead of the 10

owlstudies · Answer

i got$$2xy-5x=y+4$$

satellite73 · Answer

yup
now with 10 instead of x you subtracted y from both sides, you need to do that here

owlstudies · Answer

how would you subtract y from the side with 2xy-5x?

satellite73 · Answer

just write it is all

owlstudies · Answer

oh alright so 2xy-y-5x=4?

satellite73 · Answer

yes
now with the 20 you added 50 to both sides, with $-5x$ you have to add $5x$ to both sides (just write it )

owlstudies · Answer

2xy-y=5x+4

satellite73 · Answer

right
now here is the part that is slightly different than with the numbers

satellite73 · Answer

you had $20y-y=19y$ but here you have $xy-y$  on the left 
what you do is factor the $y$ out of the expression on the left hand side

owlstudies · Answer

ohh ok so then after you do that, you get y(2x-1)=5x+4, and then you just divide both sides by 2x-1. so then the inverse is y=(5x+4)/(2x-1)?

satellite73 · Answer

oops sorry you have $$2xy-y$$ but same idea

satellite73 · Answer

yes you got it

owlstudies · Answer

thank you so so much!!

satellite73 · Answer

or rather $$f^{-1}(x)=\frac{5x+4}{2x-1}$$  you are welcome