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

 

Option: 1

onto if f is onto
 


Option: 2

one-one if  f is one-one
 


Option: 3

continuous if f is continuous


Option: 4

None of these


Answers (1)

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(a) \text{Since} g\: (x)=|f(x)|\\ \\\therefore \: \: g(x) \geq 0\\ \\\therefore \quad g \neq R.

Hence, g is not onto.

(b) If we take f(x)=x then, f is one-one but |f(x)|=|x| is not one-one. 

(c) If f(x) is continuous then |f(x)| is also continuous. 

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Divya Prakash Singh

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