Inverse Functions

[andreac09]

I have the following function and I can't simplify the inverse. Please help!

g(x)=a+bx/c+dx

I would be super grateful!!

 

[skeeter]

I'm guessing you meant g(x) = (a + bx)/(c + dx).
Please include proper grouping symbols in your future posts.

let y = g(x) ...

y = (a + bx)/(c + dx)

swap x and y ...

x = (a + by)/(c + dy)

solve for y ...

x(c + dy) = a + by

cx + dxy = a + by

dxy - by = a - cx

y(dx - b) = a - cx

y = (a - cx)/(dx - b)

g^-1(x) = (a - cx)/(dx - b)