Question

Which of the following functions is(are) odd?

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

Answer 1

Answer: (C), (D)

(A) $ f(x)=\frac{4-x^2}{\left|x^2-4\right|}=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.