SOLUTION: Which of these is a symmetric function? A) f(x)=x^2 B) f(x)=x^3 C) f(x)=x

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Question 639432: Which of these is a symmetric function?
A) f(x)=x^2
B) f(x)=x^3
C) f(x)=x
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
A) f(x)=x
B) f(x)=x
C) f(x)=x
In each case replace f(x) by y

A)  y = x
B)  y = x
C)  y = x

Interchange the variables x and y

A)  x = y
B)  x = y
C)  x = y

For each, ask the question "Is this equivalent to what it was before the variables were interchanged?

A)  Is x = y equivalent to y = x?  Answer: NO
B)  Is x = y equivalent to y = x?  Answer: NO
C)  Is x = y  equivalent to y = x ?  Answer: YES

So the answer is C)  f(x)=x

Edwin
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