If and g(x) = x2 + 1 be two real functions, then find fog and gof.
f(x) = , g(x) = x2 + 1
Now,
Domain of f = [ – 3, ∞], domain of g = (– ∞, ∞)
Range of f = [0, ∞), range of g = [1, ∞)
Then, range of f ⊂ Domain of g and range of g ⊂ Domain of f
Hence, fog and gof exists
Now,
fog(x) = f(g(x)) = f(x2 + 1)
⇒ fog(x) =
Again,
gof(x) = g(f(x)) = g(
⇒ gof(x) =
⇒ gof(x) = x + 4