JEE Main2012MathematicsFunctionsActual

The range of the function f(x)= x 1+|x| , x R , is

Options

AR
B(-1,1)
CR- 0
D[-1,1]

Correct answer

B. (-1,1)

Step-by-step solution

f(x)= x 1+|x| , x R If x>0,|x|=x f(x)= x 1+x which is not defined for x=-1 If x < 0,|x|=-x f(x)= x 1-x which is not defined for x=1 Thus f(x) defined for all values of R except 1 and -1 Hence, range =(-1,1) .

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