Reverse function 10^x+5^x+1 ?

Question

10^x+5^x+1

Answer 1

I am not sure what you are asking.  

 

Are you asking:  Does f(x) = 10^x+5^x+1 have an inverse function?

 

Here is an answer to that question:

 

f'(x) = (ln10)10^x+(ln5)5^x > 0 for all x

 

So, f(x) is an increasing function.

 

Consequently, f(x) is one to one.

 

Therefore, f(x) has an inverse function.