Answer
$a.\quad 5$
$b.\quad-1$
$c.\quad x^{2}-6x+10$
$d.\quad x^{2}-2$
Work Step by Step
$(f\circ g)(x)=f[g(x)]=[g(x)]^{2}+1$
$=(x-3)^{2}+1$
$=x^{2}-6x+9+1$
$=x^{2}-6x+10 \qquad ... \quad(c)$
$(f\circ g)(1)=1^{2}-6(1)+10=5 \qquad ... \quad(a)$
$(g\circ f)(x)=g[f(x)]=f(x)-3$
$=x^{2}+1-3$
$=x^{2}-2 \qquad ... \quad(d)$
$(g\circ f)(1)=1^{2}-2=-1 \qquad ... \quad(b)$
