Question

If f(x) = log↓2 (x + 4), what is f↑−1(3)

Answer 1

As you already know, to get the inverse of any expression, we start off by doing a switch on the variables, and then we solve for "y".

$\bf \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad a^{log_a x}=x\\\\ -------------------------------\\\\ \stackrel{f(x)}{\underline{y}}=log_2(x+4)\qquad \qquad \stackrel{inverse}{x=log_2(\underline{y}+4)} \\\\\\ 2^x=2^{log_2(y+4)}\implies 2^x=y+4\implies 2^x-4=\stackrel{f^{-1}(x)}{y} \\\\\\ 2^3-4=f^{-1}(3)\implies 8-4=f^{-1}(3)\implies 4=f^{-1}(3)$