Question

If $F\left(x\right)=3x^4-5x^2+k$, where $k$ is a constant, is an even function, then find the value of $k$.

Answer 1

$F\left(x\right)=3x^4-5x^2+k$ is an even function.
$F(-x)=3(-x{)}^4-5(-x{)}^2+k=3x^4-5x^2+k=f\left(x\right)$ which is even
$\therefore$ It is not depending on k and it holds the same for any value of k
$\therefore$ k can be any real number.