Let f(x) = -1 + |x - 2| and g(x) = 1 - |x|. T | vedclass

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(D) Given $f(x) = -1 + |x - 2|$ and $g(x) = 1 - |x|$.We need to find the points of discontinuity for $fog(x) = f(g(x))$.$fog(x) = f(1 - |x|) = -1 + |(

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an empty set

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(D) Given $f(x) = -1 + |x - 2|$ and $g(x) = 1 - |x|$.We need to find the points of discontinuity for $fog(x) = f(g(x))$.$fog(x) = f(1 - |x|) = -1 + |(1 - |x|) - 2|$$= -1 + |- |x| - 1|$$= -1 + |-(|x| + 1)|$Since $|-a| = |a|$,we have $|-(|x| + 1)| = ||x| + 1|$.Since $|x| \ge 0$,$|x| + 1$ is always positive,so $||x| + 1| = |x| + 1$.Thus,$fog(x) = -1 + |x| + 1 = |x|$.The function $y = |x|$ is a standard absolute value function,which is continuous for all real numbers $x \in \mathbb{R}$.Therefore,there are no points where $fog$ is discontinuous.The set of all points where $fog$ is discontinuous is an empty set.

Let $f(x) = -1 + |x - 2|$ and $g(x) = 1 - |x|$. Then the set of all points where $fog$ is discontinuous is

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