1 Answer

Signum · Answer 1 · 2023-10-31T13:47:40+0000

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:

Subtract 17:

Now we change x for y and vice-versa:

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

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