Determine if Odd, Even, or Neither f(x)=3x^2-1

Problem

ƒ(x)=3*x^2−1

Solution

1. Recall the definitions of even and odd functions. A function is even if ƒ*(−x)=ƒ(x) and odd if ƒ*(−x)=−ƒ(x)

2. Substitute −x for x in the original function to evaluate ƒ*(−x)

ƒ*(−x)=3*(−x)^2−1

3. Simplify the expression by squaring the negative term. Since (−x)^2=x^2 the expression remains unchanged.

ƒ*(−x)=3*x^2−1

4. Compare the result to the original function ƒ(x) Since ƒ*(−x)=3*x^2−1 and ƒ(x)=3*x^2−1 they are identical.

ƒ*(−x)=ƒ(x)

Final Answer

ƒ(x)=3*x^2−1* is Even

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