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(A) Given the functions $f(x) = [x]$ (greatest integer function) and $g(x) = |x|$ (modulus function).We need to evaluate $(gof)\left( -\frac{5}{3} \ri

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(A) Given the functions $f(x) = [x]$ (greatest integer function) and $g(x) = |x|$ (modulus function).We need to evaluate $(gof)\left( -\frac{5}{3} \right) - (fog)\left( -\frac{5}{3} \right)$.First,calculate $(gof)\left( -\frac{5}{3} \right) = g\left( f\left( -\frac{5}{3} \right) \right)$.Since $f(x) = [x]$,$f\left( -\frac{5}{3} \right) = [-1.666...] = -2$.Then $g(-2) = |-2| = 2$.Next,calculate $(fog)\left( -\frac{5}{3} \right) = f\left( g\left( -\frac{5}{3} \right) \right)$.Since $g(x) = |x|$,$g\left( -\frac{5}{3} \right) = \left| -\frac{5}{3} \right| = \frac{5}{3}$.Then $f\left( \frac{5}{3} \right) = [1.666...] = 1$.Finally,$(gof)\left( -\frac{5}{3} \right) - (fog)\left( -\frac{5}{3} \right) = 2 - 1 = 1$.

If $f$ is the greatest integer function and $g$ is the modulus function,then $(gof)\left( -\frac{5}{3} \right) - (fog)\left( -\frac{5}{3} \right) = $

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