$A = \{1, 2, 3, 4\}$ and $B = \{1, 2, 3, 4, 5, 6\}$ are two sets,and the function $f: A \rightarrow B$ is defined by $f(x) = x + 2$ for all $x \in A$. Then the function $f$ is:
- Abijective
- Bonto
- Cone-one
- Dmany-one
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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 |
Let $f : R \rightarrow R$ be defined as $f(x) = 3^{-|x|} - 3^x + \operatorname{sgn}(e^{-x}) + 2$ (where $\operatorname{sgn}(x)$ denotes the signum function of $x$). Then which one of the following is correct?
For $A = \{-1, -2, 3, 4\}$,the number of one-one functions from $A$ to $A$ is . . . . . . .
If $f(x) = |\sin x| + |\cos x|$ and $g(x) = [x]$,then what is the period of $h(x) = g(f(x))$,where $[.]$ denotes the Greatest Integer Function $(G.I.F.)$?
The function $f(x) = x^{2} + bx + c$,where $b$ and $c$ are real constants,describes:
MediumWBJEE 2014
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