Range of 2x+|cosx|

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right)=2\mathrm{x}+\left|\mathrm{cosx}\right| \\ \mathrm{As} \mathrm{cosx} \mathrm{ranges} \mathrm{from} -1 \mathrm{to} 1 \\ \mathrm{Hence} \left|\mathrm{cosx}\right| \mathrm{will} \mathrm{range} \mathrm{from} 0 \mathrm{to} 1 \\ \mathrm{But} \mathrm{linear} \mathrm{function} 2\mathrm{x} \mathrm{ranges} \mathrm{from} -\infty \mathrm{to} \infty , \mathrm{hence} \\ \mathrm{Range} \mathrm{of} \mathrm{f}\left(\mathrm{x}\right)=2\mathrm{x}+\left|\mathrm{cosx}\right| \mathrm{will} \mathrm{be} \left(-\infty ,\infty \right) \mathrm{i}.\mathrm{e}. \mathrm{all} \mathrm{real} \mathrm{numbers}. \end{gathered}$$

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