Question

If g(x) =x+1/x-2 what is the value of (g . h) (-3)?

8/5

5/2

15/2

18/5

Answer 1

`g(x)=\cfrac{x+1}{x-2}\hspace{5em}h(x)=4-x\hspace{5em}(g\circ h)(-3)=g( ~~ h(-3) ~~ ) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ h(-3)=4-(-3)\implies h(-3)=4+3\implies h(-3)=7 \\\\[-0.35em] ~\dotfill\\\\ g( ~~ h(-3) ~~ )\implies g(7)=\cfrac{7+1}{7-2}\implies g(7)=\cfrac{8}{5}\impliedby (g\circ h)(-3)`