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PLEASE EXPLAIN IN DETAIL PLS SO I CAN UNDERSTAND BETTER

PLEASE EXPLAIN IN DETAIL PLS SO I CAN UNDERSTAND BETTER-example-1
User Sheung
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Find the inverse function of:


f(x)=\log_3(x+17)

First, call the function y = f(x):


y=\log_3(x+17)

We have to solve for x. We need to apply the definition of logarithms:

If:


\begin{gathered} a=b^x \\ \text{ Then:} \\ \log_ba=x \end{gathered}

It can be applied in inverse order, that is, if:


\begin{gathered} x=\log_ba \\ \\ \text{ Then:} \\ \\ a=b^x \end{gathered}

Applying the definition above:


x+17=3^y

Subtract 17:


x=3^y-17

Now we change x for y and vice-versa:


y=3^x-17

Finally, substitute y for the inverse of f(x):


f^(-1)(x)=3^x-17

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