Question

Which of the following functions is(are) odd?

• A. $f(x)=\frac{4-x^2}{|x^2-4|}$
• B. $g(x)=\frac{e^{x^2}-e^{-x^2}}{e^{x^2}+e^{-x^2}}$
• C. $h(x)=\sin x-2\sin 2x-\frac{1}{3}\sin 3x+4x$
• D. $k(x)=\sqrt[3]{x}+{\tan }^{-1}x$

Answer 1

Answer: (C), (D)

(A) $f(x)=\frac{4-x^2}{|x^2-4|}=f(-x)$, which is even function.
(B) $g(x)=\frac{e^{x^2}-e^{-x^2}}{e^{x^2}+e^{-x^2}}=g(-x)$, which is even function
(C) $h(-x)=-h(x)$ so $h(x)$ is odd function.
(D) $k(-x)=-k(x)$, so $k(x)$ is odd function.