Answer
(a) $ 3x^2+1$, domain $(-\infty,\infty)$.
(b) $ 9x^2+6x+1$, domain $(-\infty,\infty)$.
(c) $ 9x+4$, domain $(-\infty,\infty)$.
(d) $ x^4$, domain $(-\infty,\infty)$.
Work Step by Step
Given $f(x)=3x+1$ and $g(x)=x^2$, we have:
(a) $f\circ g=3(x^2)+1=3x^2+1$, domain $(-\infty,\infty)$.
(b) $g\circ f=(3x+1)^2=9x^2+6x+1$, domain $(-\infty,\infty)$.
(c) $f\circ f=3(3x+1)+1=9x+4$, domain $(-\infty,\infty)$.
(d) $g\circ g=(x^2)^2=x^4$, domain $(-\infty,\infty)$.
