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(B) Given,$f(x) = [x]$ and $g(x) = |x|$.We need to find $(g \circ f)\left(\frac{-5}{3}\right)$.By definition,$(g \circ f)\left(\frac{-5}{3}\right) = g

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$2$

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(B) Given,$f(x) = [x]$ and $g(x) = |x|$.We need to find $(g \circ f)\left(\frac{-5}{3}\right)$.By definition,$(g \circ f)\left(\frac{-5}{3}\right) = g\left(f\left(\frac{-5}{3}\right)\right)$.First,calculate $f\left(\frac{-5}{3}\right) = \left[\frac{-5}{3}\right]$.Since $\frac{-5}{3} = -1.666...$,the greatest integer less than or equal to $-1.666...$ is $-2$.So,$f\left(\frac{-5}{3}\right) = -2$.Now,substitute this into $g(x)$:$(g \circ f)\left(\frac{-5}{3}\right) = g(-2) = |-2|$.Since the modulus of $-2$ is $2$,we get $(g \circ f)\left(\frac{-5}{3}\right) = 2$.

If $f$ is the greatest integer function defined on $R$ as $f(x) = [x]$ and $g$ is the modulus function defined on $R$ as $g(x) = |x|$,then the value of $(g \circ f)\left(\frac{-5}{3}\right)$ is

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