For this case we have the following function:
f (x) = e ^ x
Rewriting we have:
y = e ^ x
We apply natural logarithm to both sides:
Ln (y) = Ln (e ^ x)
For logarithmic and exponential properties:
x = Ln (y)
Rewriting:
f (x) ^ - 1 = Ln (x)
Answer:
the correct inverse function is:
f (x) ^ - 1 = Ln (x)
