Question

If f: X$\to$Y is a function defined by f(x) = $2x^2-x$, check whether the function is an odd function or even function.

Answer 1

f(x) = $2x^2$ – x ...……….. (1)

f(-x) = $2(-x{)}^2$ – (-x)

= $2x^2+x$ ………….. (2)

From (1) and (2)

f(x) $\ne$ f(-x) and f(x)$\ne$ - f(-x).

Therefore the given function f(x) = $2x^2-x$ is neither an odd function nor an even function.