Find fog and gof, if
f(x) = x + 1, g(x) = sin x
f(x) = x + 1 and g(x) = sin x
Range of f = R ⊂ Domain of g = R ⇒ gof exists
Range of g= [ – 1,1] ⊂ Domain of f ⇒ fog exists
Now,
fog(x) = f(g(x)) = f(sin x) = sin x + 1
And
gof(x) = g(f(x)) = g(x + 1) = sin(x + 1)
Hence, fog(x) = sin x + 1 and gof(x) = sin(x + 1)