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f (x )= x+ |x|, is this function a-onto? b-one one? c- odd or even What i dont get in this question is that the solution does not take negative numbers in its domain.Why ?

f (x )= x+ |x|, is this function
a-onto? 
b-one one?
c- odd or even
What  i dont get in this question is that the solution does not take negative numbers in its domain.Why ?

Grade:12

1 Answers

Sunil Kumar FP
askIITians Faculty 183 Points
6 years ago
we have
f(x)=x+!x!
when x>0
the value of the function is f(x)=2x
when x<0,the value of the function is f(x)=-x+x =0
Thus this function is onto because , every element y in Y has a corresponding element x in X such that f(x) = y.
not one-one because for x<0 all have same value that is 0.The solution does not take negative number because it has either 0 or a positive value value.

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