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Question
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x
1
f(x)
g(x)
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Solution
(b) 1 \[\text{When}, - 1 < x < 0\]
\[\text{Then}, g(x) = 1 + x - \left[ x \right]\]
\[ = 1 + x - \left( - 1 \right) = 2 + x\]
\[ \therefore f\left( g(x) \right) = 1 \]
\[\text{When}, x = 0\]
\[\text{Then}, g(x) = 1 + x - \left[ x \right]\]
\[ = 1 + x - 0 = 1 + x\]
\[ \therefore f\left( g(x) \right) = 1\]
\[\text{When}, x > 1\]
\[\text{Then}, g(x) = 1 + x - \left[ x \right]\]
\[ = 1 + x - 1 = x\]
\[ \therefore f\left( g(x) \right) = 1\]
Therefore, for each interval f(g(x)) =1
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