The function $f : N \to N$ defined by $f(x) = x - 5[\frac{x}{5}]$,where $N$ is the set of natural numbers and $[x]$ denotes the greatest integer less than or equal to $x$,is
- Aone-one and onto.
- Bone-one but not onto.
- Conto but not one-one.
- Dneither one-one nor onto.
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Similar Questions
Match the functions of List-$I$ with their nature in List-$II$ and choose the correct option.
$A$. $f: R \rightarrow R$ defined by $f(x) = \cos(112x - 37)$ $I$. Injection but not surjection $B$. $f: A \rightarrow B$ defined by $f(x) = x|x|$ when $A = [-2, 2]$ and $B = [-4, 4]$ $II$. Surjection but not injection $C$. $f: R \rightarrow R$ defined by $f(x) = (x-2)(x-3)(x-5)$ $III$. Bijection $D$. $f: N \rightarrow N$ defined by $f(n) = n+1$ $IV$. Neither injection nor surjection $V$. Composite function
| $A$. $f: R \rightarrow R$ defined by $f(x) = \cos(112x - 37)$ | $I$. Injection but not surjection |
| $B$. $f: A \rightarrow B$ defined by $f(x) = x|x|$ when $A = [-2, 2]$ and $B = [-4, 4]$ | $II$. Surjection but not injection |
| $C$. $f: R \rightarrow R$ defined by $f(x) = (x-2)(x-3)(x-5)$ | $III$. Bijection |
| $D$. $f: N \rightarrow N$ defined by $f(n) = n+1$ | $IV$. Neither injection nor surjection |
| $V$. Composite function |
Check the injectivity and surjectivity of the following function $f : N \rightarrow N$ given by $f(x) = x^{3}$.
Medium
View SolutionLet $a > 1$ and $0 < b < 1$. If $f: R \rightarrow [0, 1]$ is defined by $f(x) = \begin{cases} a^x, & -\infty < x < 0 \\ b^x, & 0 \leq x < \infty \end{cases}$,then $f(x)$ is
If $f(x) = \begin{cases} [x] & \text{if } -3 < x \leq -1 \\ |x| & \text{if } -1 < x < 1 \\ |[x]| & \text{if } 1 \leq x < 3 \end{cases}$,then the set $\{x : f(x) \geq 0\}$ is equal to
If $f: R \rightarrow R$ is defined by $f(x) = x^2 + 3x + 4$,then the function $f$ is . . . . . . .
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