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What is the correct inverse function for f(x) = /n5x?

User Alaa Osta
by
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1 Answer

3 votes

The given function is


f(x)=\ln 5x

It is important to know that the inverse function for logarithms is exponential functions. In this case, we change f(x) to y.


y=\ln 5x

Then, we isolate x


\begin{gathered} e^y=e^(\ln 5x) \\ e^y=5x \\ x=(e^y)/(5) \end{gathered}

At last, we change the variables.


y=(e^x)/(5)

The inverse function notation is


f^(-1)(x)=(e^x)/(5)^{}

Hence, the answer is B.

User Namysh
by
8.4k points

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