Answer to Question #225257 in Discrete Mathematics for Amir

Question

Question No 05: [07 marks]
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

Answer 1

g(f(x))=f(g(x))

c(ax+b)+d=a(cx+d)+b

acx+bc+d=acx+ad+b

bc+d=ad+b

f°g=g°f if and only if bc+d=ad+b