Section 1.1 : Review : Functions
34. Compute \(\left( {f \circ g} \right)\left( x \right)\) and \(\left( {g \circ f} \right)\left( x \right)\) for \(f\left( x \right) = 5x + 2\), \(g\left( x \right) = {x^2} - 14x\).
Show SolutionNot much to do here other than to compute each of these.
\[\begin{align*}\left( {f \circ g} \right)\left( x \right) & = f\left[ {g\left( x \right)} \right] = f\left[ {{x^2} - 14x} \right] = 5\left( {{x^2} - 14x} \right) + 2 = 5{x^2} - 70x + 2\\ & \\ \left( {g \circ f} \right)\left( x \right) & = g\left[ {f\left( x \right)} \right] = g\left[ {5x + 2} \right] = {\left( {5x + 2} \right)^2} - 14\left( {5x + 2} \right) = 25{x^2} - 50x - 24\end{align*}\]