If $f: N \rightarrow Z$ is defined by $f(n)=\begin{cases} 2 & \text{if } n=3k, k \in Z \\ 10 & \text{if } n=3k+1, k \in Z \\ 0 & \text{if } n=3k+2, k \in Z \end{cases}$, then $\{n \in N: f(n)>2\}$ is equal to
- A$\{3, 6, 4\}$
- B$\{1, 4, 7, \dots\}$
- C$\{4, 7, \dots\}$
- D$\{7, 10, \dots\}$
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In each of the following cases,state whether the function is one-one,onto or bijective. Justify your answer. $f : R \rightarrow R$ defined by $f(x) = 3 - 4x$.
Medium
View SolutionMatch the following:
$(A)$ $f: R \rightarrow R$ is such that $f(x)=px+q$ $(p \neq 0)$,$\forall x \in R$ $I.$ $f$ is neither one-one nor onto $(B)$ $f: R \rightarrow R^{+} \cup\{0\}$ is such that $f(x)=x^2$,$\forall x \in R$ $II.$ $f$ is both one-one and onto $(C)$ $f: N \rightarrow N$ is such that $f(n)=n^2+2n+3$,$\forall n \in N$ $III.$ $f$ is one-one but not onto $(D)$ $f: R \rightarrow R$ is such that $f(x)=2(\cos ^2 5x+\sin ^2 5x)$ $\forall x \in R$ $IV.$ $f$ is onto but not one-one $V.$ $f$ is a constant function and also a bijection
| $(A)$ $f: R \rightarrow R$ is such that $f(x)=px+q$ $(p \neq 0)$,$\forall x \in R$ | $I.$ $f$ is neither one-one nor onto |
| $(B)$ $f: R \rightarrow R^{+} \cup\{0\}$ is such that $f(x)=x^2$,$\forall x \in R$ | $II.$ $f$ is both one-one and onto |
| $(C)$ $f: N \rightarrow N$ is such that $f(n)=n^2+2n+3$,$\forall n \in N$ | $III.$ $f$ is one-one but not onto |
| $(D)$ $f: R \rightarrow R$ is such that $f(x)=2(\cos ^2 5x+\sin ^2 5x)$ $\forall x \in R$ | $IV.$ $f$ is onto but not one-one |
| $V.$ $f$ is a constant function and also a bijection |
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