Find the Inverse of f(x)= ln(e^x-5)

Question

Find the Inverse of f(x)= ln(e^x-5). Any help will be apprecaited. An answer with a stepwise explanation would be excellent.

 

Thanks in advance.

Answer 1

f(x)=ln(e^x-5), f^-1(x)=?

Let y=f(x). We need to express x in terms of y.

y=ln(e^x-5). 

 e^y=e^x-5.

e^x=e^y+5. take ln)

x=ln(e^y+5) 

In this expression, x is function (dependent variable)  and y is (independent ) variable. To make it look like as usual, we just replace x and y:  y=ln(e^x+5)

So,

f^-1(x)=ln(e^x+5).