Maths · Limits, continuity and differentiability
=\left\{\begin{array}{ll}\mathbf{1} & \boldsymbol{x} \leq-\boldsymbol{2} \\ \fra
\( \boldsymbol{g}(\boldsymbol{x})=\left\{\begin{array}{ll}\mathbf{1} & \boldsymbol{x} \leq-\boldsymbol{2} \\ \frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{x} & -\boldsymbol{2}<\boldsymbol{x}<\mathbf{4} \text { .then } \\ \sqrt{\boldsymbol{x}} & , \boldsymbol{x} \geq \mathbf{4}\end{array}\right. \)
- A. \( g \) is a continuous function
- B. all the discontinuities are removable discontinuities
- C. all the discontinuities are jump
- D. all the discontinuities are infinitt
Step-by-step solution
The function g(x) has a discontinuity at x = -2 because the left-hand limit is 1 and the right-hand limit is -1, which are finite but unequal, making it a jump discontinuity. At x = 4, the function is continuous. Hence, the only discontinuity is a jump discontinuity.
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