What is the inverse function of #f(x)=e^(x-5)#?

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Answer 1 · 2017-08-24T00:11:14

#f^(-1)(x) = 5+lnx #

We have:

# f(x) = e^(x-5) #

To find the inverse, #f^(-1)(x)#, let:

# y = e^(x-5) #

And we must rearrange for an explicit expression for #x#. Taking natural logarithms, we get:

# ln(e^(x-5)) = ln(y) \ \ # (assuming #y gt 0#)
# :. x-5 = lny #
# :. x = 5+lny #

Hence:

#f^(-1)(x) = 5+lnx #