Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. (5 points)
f(x) = quantity x minus eight divided by quantity x plus seven. and g(x) = quantity negative seven x minus eight divided by quantity x minus one.

Answer 1

f(x)=(x-8)/(x+7). g(x)=(-7x-8)/(x-1). Plug in g(x) into f(x), f(g(x))=[(-7x-8)/(x-1)-8]/[-7x-8)/(x-1)+7], which can be simplified as (-7x-8-8x+8)/(-7x-8+7x-7)=-15x/-15=x. Plug in f(x) into g(x), g(f(x))=[-7*(x-8)/(x+7)-8]/[(x-8)/(x+7)-1]=(-7x+56-8x-56)/(x-8-x-7)=-15x/-15=x, as desired.