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Derivative of One Function w.r.t Another

Let f x =[ x ...

Question

Let f(x)= [x] and g(x)=|x| then find (gof) (-1/3) - (fog) (1/3) .

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Solution

f(-1/3) = [-1/3] =-1

gof(-1/3) = g(f(-1/3)=g(-1) = l -1 l = 1

g(-1/3) = l -1/3 l = 1/3

fog)(-1/3) = f(g(-1/3) = f(1/3) = [1/3] = 0

gof(-1/3)- fog(1/3) = 1-0 = 1

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