Question

Find the inverse of the exponential function $f$.
$f\left(x\right)=e^{x-1}+3$

• A. $\ln (x-1)+3$
• B. $\ln (x-3)+1$
• C. $\ln (x-1)$
• D. $\ln (x-2)-3$

Answer 1

The correct option is B $\ln (x-3)+1$

Let $y=f\left(x\right)=e^{x-1}+3$ and now solve for $x$ to find the inverse of the given function.

$y=e^{x-1}+3$

$e^{x-1}=y-3$

$\ln (y-3)=x-1$

$x=\ln (y-3)+1$

Therefore, the inverse of the function in terms of $\ln (x-3)+1$.