Question

(a) Consider f : R → R, f(x) = x
2
and g : R → R, g(x) = x + 5.
(i) What is g ◦ f?
(ii) What is f ◦ g

Answer 1

$\circ$ (circle sign) denotes here a function composition.

(i) $g \circ f = g(f(x)) = g(x^2) = x^2 +5$

(ii)$f \circ g = f(g(x)) = f(x+5) = (x+5)^2 = x^2 + 10x+25$