Given functions \(f :{A}\to{B}\) and \(g :{B}\to{C}\), the composite function, \(g\circ f\), which is pronounced as “\(g\) circle \(f\)”, is defined as \[{g\circ f}:{A}\to{C}, \qquad (g\circ f)(x) = g...Given functions \(f :{A}\to{B}\) and \(g :{B}\to{C}\), the composite function, \(g\circ f\), which is pronounced as “\(g\) circle \(f\)”, is defined as \[{g\circ f}:{A}\to{C}, \qquad (g\circ f)(x) = g(f(x)). \nonumber\] The image is obtained in two steps. The functions \(f :{\mathbb{R}}\to{\mathbb{R}}\) and \(g :{\mathbb{R}}\to{\mathbb{R}}\) are defined by \[f(x) = 3x+2, \qquad\mbox{and}\qquad g(x) = \cases{ x^2 & if $x\leq5$, \cr 2x-1 & if $x > 5$. \cr} \nonumber\] Determine \(f\circ g\).
