Question

if f(x) = (x - 5) and g(x) = ( 5 - x) check if (fog)(x)= (gof) (x)

Answer 1

$HEYA \: \\ \\ (fog)(x) = f(g(x) )\\ \\ f(g(x)) = f((5 - x)) \\ \\ f((5 - x)) = (5 - x) + 5 \\ \\ f((5 - x)) = - x \\ \\ \\ and \: \\ \\ (gof)(x) = g(f(x)) \\ \\ g(f(x)) = g((x - 5)) \\ \\ g((x - 5)) = x - 5 + 5 \\ \\ g((x - 5)) = - x \\ \\ so \: \: \: (fog(x)) = (gof(x))$