Answer
a) $\dfrac{1}{x^3}$
b) $\dfrac{1}{x^3}$
c) $x$
Work Step by Step
We are given the functions:
$f(x)=x^3$
$g(x)=\dfrac{1}{x}$
a) Find $f\circ g$:
$(f\circ g)(x)=f(g(x))=f\left(\dfrac{1}{x}\right)=\left(\dfrac{1}{x}\right)^3=\dfrac{1}{x^3}$
b) Find $g\circ f$:
$(g\circ f)(x)=g(f(x))=g(x^3)=\dfrac{1}{x^3}$
c) Find $g\circ g$:
$(g\circ g)(x)=g(g(x))=g\left(\dfrac{1}{x}\right)=\dfrac{1}{\dfrac{1}{x}}=x, x \ne 0$
