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a function f(x) is defined by f(x)=x|x| when |x|>=1 and f(x)= x^2sin((pi/2)x) when |x| =1 den it should be even.

a function f(x) is defined by f(x)=x|x| when |x|>=1 and f(x)= x^2sin((pi/2)x) when |x|<1,|.| is modulus function.Whether it is odd or even???.actually in my book it is given to be odd but i thk it should depend on its defination,i mean when |x|>=1 den it should be even.

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1 Answers

jitender lakhanpal
62 Points
9 years ago

Dear Manuj,

 

f(x)= x^2sin((pi/2)x)     this is definitely odd as f(x) = -f(-x)

f(x)=x|x|     |x| >=1   is an odd we can say that just by looking the graph 

 just check the attachement for the graph    



 

 

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