Question

For the functions ​f(x)=x−1 and ​g(x)=5x find the following.
​(a)​ (f◦​g)(x) and its domain
​(b)​ (g◦​f)(x) and its domain

Answer 1

Part (a)

$(f \circ g)(x)=f(g(x))=f(5x)=\boxed{5x-1}$

This is a linear function, so the domain is all real numbers.

Part (b)

$(g \circ f)(x)=g(f(x))=g(x-1)=5(x-1)=\boxed{5x-5}$

This is a linear function, so the domain is all real numbers.