Find fog and gof, if

f(x) = x², g(x) = cos x

f(x)= x, g (x) = cos x

Domain of f and Domain of g = R

Range of f = (0, ∞)

Range of g = (– 1,1)

∴ Range of f ⊂ domain of g ⇒ gof exist

Also, Range of g ⊂ domain of f ⇒ fog exist

Now,

gof (x) = g (f (x)) = g (x²) = cos x²

And

fog (x) = f(g(x)) = f (cos x) = cos² x

Hence, fog(x) = cos x² and gof(x) = cos² x