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MAVERICK [17]
2 years ago
10

Find the inverse

}^{3x - 1} " alt="f(x)={e}^{3x - 1} " align="absmiddle" class="latex-formula">
Tank you for your support ​
Mathematics
1 answer:
FromTheMoon [43]2 years ago
8 0

Answer:

f^{-1}(x)=\dfrac{1}{3}(\ln x +1)

Step-by-step explanation:

Given function:

f(x)=e^{3x-1}

Replace f(x) with y:

\implies y=e^{3x-1}

Take natural logs of both sides:

\implies \ln y = \ln e^{3x-1}

Apply the Power Log Law   \ln x^n=n\ln x :

\implies \ln y = (3x-1)\ln e

As \ln e=1 then:

\implies \ln y = 3x-1

Rearrange to make x the subject:

\implies 3x=\ln y +1

\implies x=\dfrac{1}{3}(\ln y +1)

Swap x for f^{-1}(x)  and y for x:

\implies f^{-1}(x)=\dfrac{1}{3}(\ln x +1)

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