Let f (x) = ax + b and g(x) = cx + d, where a, b, c, and d are constants. determine necessary and sufficient conditions on the constants a, b, c, and d so that f ◦ g = g ◦ f
In order for [tex]f\circ g=g\circ f[/tex] to hold, we require [tex]ad+b=bc+d[/tex], which can be rearranged slightly as [tex](a-1)d=(c-1)b[/tex] or [tex]\dfrac{a-1}{c-1}=\dfrac bd[/tex], etc.
