Question

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

• A. $k$ is an integer
• B. $k$ is a fraction
• C. $k$ is irrational
• D. $k$ is natural.

Answer 1

Answer: (A), (B), (C), (D)

$k$ is natural.

If $f\left(x\right)=3x^4-5x^2+k$ 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.
$\therefore k$ can be integer, fraction, irrational or a natural number.