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MHT CET202618 April 2026Evening ShiftMathematicsFunctionsActual

The domain of the function f(x) = x 1+x is

Options

  1. A(- ,-1) [0, )
  2. B(- ,-1] [0, )
  3. C(- ,-1) [0, )
  4. Dall R

Correct answer

A. (- ,-1) [0, )

Step-by-step solution

For f(x) to be defined, the expression under the square root must be non-negative and the denominator must not be zero. x 1+x 0 and 1+x 0 The critical points are x = 0 and x = -1 . Using the sign scheme for x 1+x : For x (- , -1) , x 1+x > 0 For x (-1, 0) , x 1+x For x [0, ) , x 1+x 0 Since x = -1 makes the denominator zero, it is excluded from the domain. The domain is (- , -1) [0, ) . Answer: (- ,-1) [0, )

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