Question

Is the function 𝑓:𝑹 →R defined as f:(x) = (x — 7) (x^3 + 11)is an odd function.

Answer 1

$f(x) = (x - 7) (x^3 + 11) \\f(-x) = (-x-7)[(-x)^3+11)] \\=-(x+7)(-x^3+11) \\=-(x+7)(11-x^3)\neq-f(x)$

For $f(x)$ to be an odd function: $f(-x)=-f(x)$

But, there is no relation between $f(x)$ and $f(-x)$ here in this problem.

So, $f(x)$ is not an odd function.