Question

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

Answer 1

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)`