If and are defined by =\boldsymbol{x}-[\boldsymbol{x}] \) and =[\boldsymbol{x}] \) for where \) is the greatest integer not exceeding then for every )= \)

Maths · The composition of functions

If and are defined by =\boldsymbol{x}-[\boldsymbol{x}] \) and =[\boldsymbol{x}]

If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) are defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}-[\boldsymbol{x}] \) and \( \boldsymbol{g}(\boldsymbol{x})=[\boldsymbol{x}] \) for \( \boldsymbol{x} \in \boldsymbol{R}, \) where \( [\boldsymbol{x}] \) is the greatest integer not exceeding \( x, \) then for every \( x \in \) \( \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x}))= \)

A. \( x \)
B. 0
C. \( f(x) \)
D. \( g(x) \)

Step-by-step solution

Given f(x) = x - [x] and g(x) = [x], then f(g(x)) = f([x]) = [x] - [[x]] = [x] - [x] = 0.

Practise more in this unit View MCQs Sign up for full question bank

Let =\mathbf{2}^{100} \boldsymbol{x}+\mathbf{1} \) =\boldsymbol{3}^{100} \boldsymbol{x}+\mathbf{1} \) Then the set of real numbers x such th…
Read the following information and answer the three items that follow: Let =\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}-\boldsymbol{5} …
If is defined by =\boldsymbol{2} \boldsymbol{x}- \) 2, then (x)+2= \)…
Assertion Let and be increasing and decreasing functions respectively from \) to . \operatorname{Let} h(x)=f(g(x)) . \) If =0, \) then \) is…

Step-by-step solution

Related MCQs