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