# Math

Help me for this question on composite functions

Does the composition of functions display the commutative property? Give an example of each case to illustrate your answer.

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1. not usually, even for linear functions:

f = ax+b
g = cx+d

f◦g = ag+b = a(cx+d)+b = acx + ad+b
g◦f = cf+d = c(ax+b)+d = acx + bc+d

with suitable values for a,b,c,d it might work.

For other functions, all bets are off

f = e^x
g = x^2

f◦g = e^g = e^(x^2)
g◦f = f^2 = e^(2x)

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