Question

If f(x)=3x+2 and g(x)=x^2-3x-4, what is (g0f)(5)

Answer 1

$\bf \begin{cases} f(x)=3x+2\\ g(x)=x^2-3x-4\\[-0.5em] \hrulefill\\ (g\circ f)(5)=g(~~f(5)~~) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(5)=3(5)+2\implies f(5)=17 \\\\[-0.35em] ~\dotfill\\\\ g(~~f(5)~~)\implies g(~~17~~)=(17)^2-3(17)-4\implies g(17)=289-58-4 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{(g\circ f)(5)}{g(17)=227}~\hfill$