Question

What is the domain of the composite function of f(x)=x^2 and g(x)=sin x when (g o f)(x) and (f o g)(x)??


when i joined the two function it looks the same to me..

Answer 1

(g o f)(x)
= g (f(x) )
= g(x^2)
= sin (x^2)

domain: any real x

(f o g)(x)
= f (g(x) )
= f(sinx)
= (sinx)^2 or sin^2 x

domain: any x

Answer 2

thank you!