Determining even functions

[KJ2569]

Hello.

I need help to determine whether or not a function is even. I'd also like to get an explanation of that determination as I'm not getting a clear picture from my book or class notes. In the following problem, is the function even because the exponents are even? Is that all it boils down to?

Directions: Determine whether the following functions are even f(-k)=f(k).

Problem:

g(x)=1/3x^4-5x^2+1

Thank you.

KJ

 

[pka]

Directions: Determine whether the following functions are even f(-k)=f(k).
Problem:
g(x)=1/3x^4-5x^2+1

\(\displaystyle g(-k)=\frac{1}{3}(-k)^4-5(-k)^2+1=~?\)

Now \(\displaystyle g(k)=~?\)

 

[KJ2569]

Thank you.

Thanks! It's much clearer now. I think I just hit a wall & wasn't thinking clearly.

Now I see:

g(-k) = 1/3k⁴- 5k² + 1

g(k) = 1/3 (k)⁴ - 5 (k)² + 1

= 1/3k⁴ - 5k² + 1

so:

g(-k) = g(k); the function is even.