TS EAMCET · Maths · Functions
If \(f: \mathbb{R} \rightarrow \mathbb{R}\) is defined by \(f(\mathrm{x})=2 \mathrm{x}+\sin \mathrm{x}, \mathrm{x} \in \mathrm{R}\), then \(f\) is
- A one-one and onto
- B one-one but not onto
- C onto but not one-one
- D neither one-one nor onto
Answer & Solution
Correct Answer
(A) one-one and onto
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & f(x)=2 x+\sin x \\ & f^{\prime}(x)=2+\cos x>0 \end{aligned} \] \(\therefore f(x)\) is one-one. \(\because \quad \forall y \in f(x)\), there exist some \(x\) as there is a polynomial function \(2 x\). \(\therefore f(x)\) is onto.
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