f(x)=x-[x] in the interval [0,1] is - Vidyadip

Question

$f(x)=x-[x]$ in the interval $[0,1]$ is

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Answer

(a) : Given $f(x)=x-[x], x \in[0,1]$
But for $0 \leq x \leq 1,[x]=0, \therefore f(x)=x-0=x$ in $[0,1]$.
Let $x_1, x_2 \in[0,1]$ be such that $x_1$ < $x_2$
=> $f\left(x_1\right)$ < $f\left(x_2\right)$ => $f$ is increasing in $[0,1]$.

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