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Let \mathrm{f: R \rightarrow R}  be any function. Also, \mathrm{g: R \rightarrow R} is defined by \mathrm{g(x)=|f(x)|} for all \mathrm{x}. Then \mathrm{g} is

Option: 1

 onto if f is onto


Option: 2

one-one if f is one-one


Option: 3

 continuous if fis  continuous 


Option: 4

None of these


Answers (1)

best_answer

\mathrm{Since \: g(x)=\mid f(x)}

\mathrm{ \text { Since } g(x)=|f(x)| }
\mathrm{ \therefore \quad g(x) \geq 0}


\mathrm{ \therefore \text { Range of } g \neq R \text {. Hence, } g \text { is not onto. }}

(b) If we take \mathrm{f(x)=x}, then \mathrm{f}  is one-one but \mathrm{|f(x)|=|x|} is not one-one.
(c) If \mathrm{f(x)} is continuous then \mathrm{|f(x)|} is also continuous.

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Riya

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