Answered

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

Sagot :

The given function is

[tex]f(x)=\ln 5x[/tex]

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

[tex]y=\ln 5x[/tex]

Then, we isolate x

[tex]\begin{gathered} e^y=e^{\ln 5x} \\ e^y=5x \\ x=\frac{e^y}{5} \end{gathered}[/tex]

At last, we change the variables.

[tex]y=\frac{e^x}{5}[/tex]

The inverse function notation is

[tex]f^{-1}(x)=\frac{e^x}{5}^{}[/tex]

Hence, the answer is B.

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