Asked by Chris

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.

Answers

Answered by Steve
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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