f(x) = (x-8)/(x+7) and g(x) = (-7x-8)/(x-1)
To confirm that f(x) and g(x) are inverses.
f(g(x)) = x
g(f(x)) = x
f(g(x)) = (((-7x-8)/(x-1))-8)/(((-7x-8)/(x-1))+7)
f(g(x)) = (-15x² -15x)/(-15x² - 15)
f(g(x)) = -15x/-15
f(g(x)) = x
g(f(x)) = (-7((x-8)/(x+7))-8)/(((x-8)/(x+7))-1)
g(f(x)) = (-15x² - 105x)/(-15x²- 105)
g(f(x)) = -105x/-105
g(f(x)) = x
f(x) and g(x) are inverses.