Let f(x) = 4x^2–6 and g(x)=x–2.(a) Find the composite function (f@g)(x) and simplify. Show work.(b) Find (f@g)(−1). Show work.

(a) The composite function is,
${\displaystyle (f\circ g)\left(x\right)=f\left(g\left(x\right)\right)}$
${\displaystyle =f(x-2)}$
${\displaystyle =4{(x-2)}^2-6}$ [replacing x by $x-2\in f(x)$]
${\displaystyle =4(x^2-4x+4)-6}$
${\displaystyle =4x^2-16x+16-6}$
${\displaystyle 4x^2-16x+10}$
b) Replacing x by -1 in the composite function, we get
${\displaystyle (f\circ g)(-1)=4{(-1)}^2-16(-1)+10}$
$=4+16+10$
$=30$