Question

Under what circumstances is fog = gof always true? When is this statement true for f(x) = x2 + x – 2 and g(x) = x + 4? (4 marks)

Answer 1

X^2***

Answer 2

It is true when f(x) and g(x) are inverses of each other, that is,
f(g(x)) = g(f(x)) = x

for f(x) = x^2 + x – 2 and g(x) = x + 4, since x+4 is clearly not the inverse of f(x) fog ≠ gof