Mathematics - Functions Question with Solution | TestHub

Given,$f\left(x\right)=x-5\left[\frac{x}{5}\right]$

Hence,$f\left(x\right)=5\left(\frac{x}{5}-\left[\frac{x}{5}\right]\right)$

$=5\left\{\frac{x}{5}\right\}$

Since,$x$is a natural number.

Hence,$\left\{\frac{x}{5}\right\}=0,\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5}$

Hence,$f\left(x\right)=0$, when$x=5n, n\in N$

$=1$when$x=5n+1, n\in N$

$=2$when$x=5n+2, n\in N$

$=3$when$x=5n+3, n\in N$

$=4$when$x=5n+4, n\in N$

Hence,$f\left(x\right)$is neither one-one nor onto.