Is the composite function g ◦ f is a constant function if: f(x) = [x

1.	Is the composite function g ◦ f is a constant function if: f(x) = [x] and g(x) = x − [x], where [x] denotes the largest integer less than or equal to x ?
Answer» Yes the given composite function is a constant function. f(x) = [x] GIF g(x)= x-[x] = {x} Fractional part function GoF = {[x]} We know [x] always give integer, and we also that fractional part of integer is 0. Hence gof always give 0 as answer. f(x) = [x], g(x) = x-[x] (gof) (x) = g(f(x)) = f[x] = [x] - [[x]] = [x] - [x] = 0 Hence, gof is a zero function which is a constant function.

Is the composite function g ◦ f is a constant function if: f(x) = [x] and g(x) = x − [x], where [x] denotes the largest integer less than or equal to x ?

Answer»

Yes the given composite function is a constant function.

f(x) = [x] GIF

g(x)= x-[x] = {x} Fractional part function

GoF = {[x]}

We know [x] always give integer, and we also that fractional part of integer is 0.

Hence gof always give 0 as answer.

f(x) = [x], g(x) = x-[x]

(gof) (x) = g(f(x)) = f[x] = [x] - [[x]]

= [x] - [x]

= 0

Hence, gof is a zero function which is a constant function.

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Is the composite function g ◦ f is a constant function if: f(x) = [x] and g(x) = x − [x], where [x] denotes the largest integer less than or equal to x ?

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