Answer
a) $3x^4$
b) $81x^4$
c) $x^{16}$
Work Step by Step
We are given the functions:
$f(x)=3x$
$g(x)=x^4$
a) Find $f\circ g$:
$(f\circ g)(x)=f(g(x))=f(x^4)=3(x^4)=3x^4$
b) Find $g\circ f$:
$(g\circ f)(x)=g(f(x))=g(3x)=(3x)^4=81x^4$
c) Find $g\circ g$:
$(g\circ g)(x)=g(g(x))=g(x^4)=(x^4)^4=x^{16}$
