Question

Please please help show all work

Answer 1

to find the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for the dependent variable, usually y.

$\bf 1) \\\\\\ F(x)=2x-3\implies \stackrel{\downarrow }{y}=2x-3 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 2) \\\\\\ \stackrel{\textit{switcheroo on the variables}}{\underline{x}=2\underline{y}-3}\implies x+3=2y\implies \cfrac{x+3}{2}=y~~\impliedby G(x)$

3)

now, we do the same for G(x), to get its inverse

$\bf \stackrel{G(x)}{y}=\cfrac{x+3}{2}\implies \stackrel{\textit{quick switcheroo}}{\underline{x}=\cfrac{\underline{y}+3}{2}}\implies 2x=y+3\implies 2x-3=y\impliedby F(x)$