Inverse of a non-trivial exponential function I am asked to determine the inverse function of this function,
    $$f(x)=2^{x}+3^{x}$$
The inverse function can not be found explicitly, since there is no way to explicitly clear x, but this does not mean that it has no inverse.
I could show a way to find the inverse of this function
Edit  How can we find the inverse of this function with the problems that it presents in the clearance of the x?

You could, for example, write the solution to $2^x + 3^x = y$ as a series in powers of $y-2$:
$$\eqalign{x &= \frac{y-2}{\ln(6)} - \left(\ln(3)^2 + \ln(2)^2\right) \frac{(y-2)^2}{2 \ln(6)^3}\cr +& \left(2 \ln(3)^4 - \ln(3)^3\ln(2)+6\ln(3)^2\ln(2)^2-\ln(3)\ln(2)^3 + 2 \ln(2)^4\right)\frac{(y-2)^3}{6 \ln(6)^5}\cr - &\left(3 \ln(3)^6 - 4 \ln(3)^5 \ln(2) + 18 \ln(3)^4 \ln(2)^2 - 10 \ln(3)^3 \ln(2)^3 + 18 \ln(3)^2 \ln(2)^4 - 4 \ln(3)\ln(2)^5 + 3 \ln(2)^6 \right) \frac{(y-2)^4}{12 \ln(6)^7}
\cr + &\ldots }$$
