\( 1<\quad \) Given that \( f(x)=4 x+1 \) and \( g(x)=x^{3} \), find \( (f \circ g)(-2) \)

To find \((f \circ g)(-2)\), we need to first understand that the notation \((f \circ g)(x)\) represents the composition of the functions \(f\) and \(g\). This means that we first apply \(g\) to \(x\) and then apply \(f\) to the result. Given \(f(x) = 4x + 1\) and \(g(x) = x^3\), we have: 1. Apply \(g\) to \(-2\): \[ g(-2) = (-2)^3 = -8 \] 2. Now apply \(f\) to the result of \(g(-2)\): \[ f(g(-2)) = f(-8) = 4(-8) + 1 = -32 + 1 = -31 \] Therefore, \((f \circ g)(-2) = -31\).