Answer
a) $x^2-2x+1$
b) $x^2-1$
c) $x-2$
Work Step by Step
We are given the functions:
$f(x)=x^2$
$g(x)=x-1$
a) Find $f\circ g$:
$(f\circ g)(x)=f(g(x))=f(x-1)=(x-1)^2=x^2-2x+1$
b) Find $g\circ f$:
$(g\circ f)(x)=g(f(x))=g(x^2)=x^2-1$
c) Find $g\circ g$:
$(g\circ g)(x)=g(g(x))=g(x-1)=(x-1)-1=x-2$
