Question

Let g(x) = 5x -2 and h(x)= x^2-16

1. (h"Composition"g) (-1)
This is the best I can do with explaining this. If anyone could please help and explain this to me, I would really appreciate it. The composition thing is just an open circle between the two..

Answer 1

`\bf \begin{cases} g(x)=5x-2\\ h(x)=x^2-16 \end{cases}\qquad (h\circ g)(x)\implies h(~g(x)~) \\\\\\ g(\stackrel{\downarrow }{-1})=5(\stackrel{\downarrow }{-1})-2\implies g(-1)=-5-2\implies \boxed{g(-1)=-7}\\\\ -------------------------------\\\\ (h\circ g)(-1)\implies h(~g(-1)~)\implies h\left( \boxed{-7} \right) \\\\\\ h(\stackrel{\downarrow }{-7})=(\stackrel{\downarrow }{-7})^2-16\implies h(-7)=49-16\implies \stackrel{(h\circ g)(-1)}{h(-7)=33}`