Find fog and gof, if

f(x) = c, c ∈ R, g(x) = sin x²

f(x) = c, c ∈ R and

g(x) = sin x²

Range of f = R ⊂ Domain of g = R ⇒ gof exists

Range of g= [ – 1,1] ⊂ Domain of f =R ⇒ fog exists

Now,

gof(x) = g(f(x)) = g(c) = sin c² and

fog(x) = f (g(x))= f(sin x²) =c

Thus, gof(x) = sin c² and fog(x) = c