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TiliK225 [7]
3 years ago
10

If f(x) = log2 (x + 4), what is f−1(3)?

Mathematics
1 answer:
Kaylis [27]3 years ago
7 0
Now, to get the inverse "relation", we first, do a quick switcharoo on the variables, and then solve for "y".

\bf f(x)=y=log_{2}(x+4)\qquad inverse\implies \boxed{x}=log_{2}\left(\boxed{y}+4  \right)\\\\
-------------------------------\\\\
\textit{Logarithm Cancellation Rules}\\\\
log_{{  a}}{{  a}}^x\implies x\qquad \qquad 
{{  a}}^{log_{{  a}}x}=x\\
~~~\qquad \qquad \qquad \qquad \qquad \uparrow \\
~\qquad \qquad \qquad \textit{let's use this rule}\\\\
-------------------------------\\\\


\bf 2^x=2^{\cfrac{}{}log_{2}(y+4)}\implies 2^x=y+4\implies 2^x-4=y\impliedby f^{-1}
\\\\\\
thus\qquad 2^3-4=f^{-1}(3)\implies 8-4=f^{-1}(3)\implies 4=f^{-1}(3)
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