Answer
$a.\quad-24$
$b.\quad 65$
$c.\quad 10x^{2}-3$
$d.\quad 50x^{2}+20x-5$
Work Step by Step
$(f\circ g)(x)=f[g(x)]=5[g(x)]+1$
$=5(2x^{2}-7)+1$
$=10x^{2}-35+1$
$=10x^{2}-34 \qquad ... \quad(c)$
$(f\circ g)(1)=10(1)^{2}-34=-24 \qquad ... \quad(a)$
$(g\circ f)(x)=g[f(x)]=2[f(x)]^{2}-7$
$=2(5x+1)^{2}-7$
$=2(25x^{2}+10x+1)-7$
$=50x^{2}+20x+2-7$
$=50x^{2}+20x-5 \qquad ... \quad(d)$
$(g\circ f)(1)=50(1^{2})+20(1)-5=65 \qquad ... \quad(b)$
