\( \left. \begin{array} { l } { f ( x ) = 2 x - 9 } \\ { g ( x ) = - 5 x + 6 } \\ { ( g \circ f ) ( x ) = g ( f ( x ) ) } \end{array} \right. \)

Did you know that function composition has been a key concept in mathematics since the 17th century? Mathematicians like Descartes and Leibniz explored relationships between functions long before the advent of calculators. Today, we use function composition in various fields such as physics, engineering, and computer science to model complex systems and make calculations simpler and more efficient. To put your skills to the test, try evaluating the composition \( (g \circ f)(x) \) step by step! Start by substituting \( f(x) = 2x - 9 \) into \( g(x) = -5x + 6 \). Make sure to carefully handle the substitution — it's a common mistake to forget to replace the variable correctly! So, \( g(f(x)) \) becomes \( g(2x - 9) = -5(2x - 9) + 6 \). Give it a shot!