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