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

Algebra ->  Test  -> Lessons -> SOLUTION: Which of these is a symmetric function? A) f(x)=x^2 B) f(x)=x^3 C) f(x)=x      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
A) f(x)=x²
B) f(x)=x³
C) f(x)=x
In each case replace f(x) by y

A)  y = x²
B)  y = x³
C)  y = x

Interchange the variables x and y

A)  x = y²
B)  x = y³
C)  x = y

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

A)  Is x = y² equivalent to y = x²?  Answer: NO
B)  Is x = y³ equivalent to y = x³?  Answer: NO
C)  Is x = y  equivalent to y = x ?  Answer: YES

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

Edwin