Inverse function: Find the inverse of f(x) = 3^{ x / (x - 1) }

[zuzu365]

Hallo does someone know how to make inverse function to this function?
f(x)= 3^(x/(x-1))
i do have the answer but i dont know how it was done so if someone culd explain the steps i would be very thankful

 

[Dr.Peterson]

Hallo does someone know how to make inverse function to this function?
f(x)= 3^(x/(x-1))
i do have the answer but i dont know how it was done so if someone culd explain the steps i would be very thankful

I'd like to see what you can do with it, and where you got stuck. I presume you know the basic idea of finding an inverse, which starts with replacing f(x) with y. The trouble probably comes in solving the resulting equation.

If you just need a start, I would take the log of both sides first.

From there, at some point you will probably have an equation that looks like "something" = x/(x-1). This is a rational equation, and can be solved by methods you should have learned for those. One approach is to multiply both sides by (x-1), which makes it a linear equation; or you might see a different way. (This is why I can't just "explain the steps" -- there isn't just one way to do the whole thing, and what I told you might not turn out to be the best given what you have learned.)

When you write back, show what you have done, so we can tell where you need help.

By the way, thanks for carefully using parentheses -- that saves a couple steps of clarifying what the problem is!

 

[stapel]

does someone know how to make inverse function to this function?

f(x)= 3^(x/(x-1))

i do have the answer but i dont know how it was done so if someone culd explain the steps i would be very thankful

What was the process (the sequence of steps) they gave you in class for finding the inverse of a function? How far have you gotten in applying those steps? You renamed "f(x)" as "y" and... then what?

Please be complete. Thank you!