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.
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)
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)
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.