Question

Find the inverse function of

f(x)= (1+3x)/(5-2x)

Answer 1

Start with x=(1+3y)/(5-2y)
and solve for y.

Answer 2

This^

Answer 3

x=(1+3y)/(5-2y)

x(5-2y)=(1+3y)

5x-2xy-1=3y

y= (5x-2xy-1)/3

Answer 4

You still have a y on the right side of the =. You need to get it isolated on one side.
Try getting all the groups of y on one side, then factoring it out.

Answer 5

please help me this is where i struggle

Answer 6

OK, this step is still fine:
5x-2xy-1=3y
Get all the groups of y on one side, and the rest of the junk on the other:
-2xy-3y=1-5x

Answer 7

Now factor out y from the left side.

Answer 8

ok y(-2x-3)=1-5x

Answer 9

y=1-5x/(-2x-3)

Answer 10

Yep, and if you wanna get all fancy, you can factor out a -1 from the denominator to get
\[f^{-1}(x)=-\frac{1-5x}{2x+3}\]

Answer 11

Or \[f^{-1}(x) = \frac{5x-1}{2x+3}\]Looks better. Just saying.

Answer 12

wait so how do u get the inverse?

Answer 13

Just replace the y and x to each other then solve for y.

http://www.mathsisfun.com/sets/function-inverse.html

Answer 14

@micahwood50 true, true.

Answer 15

anyway use this formula will work too :
if given f(x) = (ax+b)/(cx+d), so
f^(-1)(x) = (-dx+b)/(cx-a)
for ilustration,, look here