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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