Answer
$a.\quad 31$
$b.\quad 27$
$c.\quad 48x^{2}-24x+7$
$d.\quad 12x^{2}+15 $
Work Step by Step
$(f\circ g)(x)=f[g(x)]=3[g(x)]^{2}+4$
$=3(4x-1)^{2}+4$
$=3(16x^{2}-8x+1)+4$
$=48x^{2}-24x+3+4$
$=48x^{2}-24x+7 \qquad ... \quad(c)$
$(f\circ g)(1)=48(1)^{2}-24(1)+7=31 \qquad ... \quad(a)$
$(g\circ f)(x)=g[f(x)]=4[f(x)]-1$
$=4(3x^{2}+4)-1$
$=12x^{2}+16-1$
$=12x^{2}+15 \qquad ... \quad(d)$
$(g\circ f)(1)=12(1^{2})+15=27 \qquad ... \quad(b)$
