Determine if Odd, Even, or Neither f(x)=x^2

Problem

ƒ(x)=x2

Solution

1. Recall the definitions for function parity: a function is even if ƒ*(−x)=ƒ(x) and it is odd if ƒ*(−x)=−ƒ(x)

2. Substitute −x into the function in place of x to evaluate ƒ*(−x)

ƒ*(−x)=(−x)2

3. Simplify the expression by applying the property that any negative number squared results in a positive value.

(−x)2=x2

4. Compare the result to the original function. Since x2 is the original ƒ(x) the condition for an even function is met.

ƒ*(−x)=ƒ(x)

Final Answer

ƒ(x)=x2* is Even

Want more problems? Check here!