Answer to Question #72831 in Algebra for Dwaylon

Question

Let S be the set of all real numbers. Define f: S ~
9.
S by f(s) = S2, and
g: S ~ S by g(s) = s + 1.
(a) Find fog.
(b) Find g 0 f.
(c) Isfog = gof?

Answer 1

(a) f∘g(s)=f(s+1)=(s+1)^2=2s^2+2s+1.
(b) g∘f(s)=g(s^2 )=s^2+1.
(c) h(s)≔f∘g(s)-g∘f(s)=2s^2+2s+1-s^2-1=s^2+2s, h(1)=3≠0.