Question

Can someone tell me how i find this problem?

Answer 1

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

`\stackrel{f(x)}{y}~~ = ~~\cfrac{x+5}{x+7}\hspace{10em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~\cfrac{y+5}{y+7}} \\\\\\ xy+7x=y+5\implies xy-y+7x=5\implies xy-y=5-7x \\\\\\ \stackrel{\textit{common factoring}}{y(x-1)=5-7x}\implies y=\cfrac{5-7x}{x-1}=f^(-1)(x) \\\\[-0.35em] ~\dotfill\\\\ f^(-1)(-8)~~ = ~~\cfrac{5-7(-8)}{(-8)-1}\implies f^(-1)(-8)=\cfrac{61}{-9}\implies f^(-1)(-8)=-6(7)/(9)`