Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function defined by $f(x)=|x|+2 x$ for $x \in \mathbb{R}$. Then $f$ is

• A

  one-to-one but not onto
• B

  invertible and $f^{-1}(x)=-|x|+\frac{x}{2}$ for $x \in \mathbb{R}$
• C

  onto but not one-to-one
• Correct answer
  D

  invertible and $f^{-1}(x)=-\frac{|x|}{3}+\frac{2 x}{3}$ for $x \in \mathbb{R}$

Hence, the correct answer is option: 'D'.