If $f: N \rightarrow Z$ is defined by $ f(n)=\left\{\begin{array}{l} 2 \text { if } n=3 k, k \in Z \\ 10…
If $f: N \rightarrow Z$ is defined by
$
f(n)=\left\{\begin{array}{l}
2 \text { if } n=3 k, k \in Z \\
10 \text { if } n=3 k+1, k \in Z \\
0 \text { if } n=3 k+2, k \in Z
\end{array}\right.
$
Then , $\{n \in N: f(n)>2\}$ is equal to
$\{3,6,4\}$
$\{1,4,7\}$
$\{4,7\}$
$\{7\}$
Solution
We have,
$
f(n)= \begin{cases}2 & \text { if } n=3 k, k \in Z \\ 10 & \text { if } n=3 k+1, k \in Z \\ 0 & \text { if } n=3 k+2, k \in Z\end{cases}
$
For $f(n)>2$, we take $n=3 k+1, k \in Z$
$
\begin{aligned}
& \Rightarrow \quad n=1,4,7 \\
& \therefore \text { Required set }\{n \in Z ; f(n)>2\} \\
& =\{1,4,7\} \\
&
\end{aligned}
$