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RELATIONS AND FUNCTIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSRELATIONS AND FUNCTIONS1 Mark
Question
State True or False for the statements.
Let f : R → R be the function defined by $\text{f}(\text{x})=\sin(3\text{x}+2)\ \forall\ \text{x}\in\text{R}.$ Then f is invertible.
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Answer

False.
Solution:
The first condition for any function to be invertible is that it should be one-one function.
The given function i.e., $\text{f}(\text{x})=\sin(3\text{x}+2)\ \forall\ \text{x}\in\text{R}$ is not one-one function for all $\text{x}\in\text{R}$
Hence, f is not invertible.

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