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Question

If f colon N not stretchy rightwards arrow Z is defined by f space left parenthesis n right parenthesis equals open curly brackets table attributes columnalign center left left columnspacing 1em end attributes row cell bold 2 comma end cell cell text  if  end text bold n equals 3 bold k comma end cell cell bold k element of bold Z end cell row cell bold 10 minus bold n comma end cell cell text  if  end text bold n equals 3 bold k plus bold 1 comma end cell cell bold k element of bold Z text  then  end text left curly bracket n element of N colon f left parenthesis n right parenthesis greater than 2 right curly bracket equals end cell row cell bold 0 comma end cell cell text  if  end text bold n equals 3 bold k plus bold 2 comma end cell cell bold k element of bold Z end cell end table close

  1. left curly bracket 3 comma 6 comma 4 right curly bracket
  2. left curly bracket 1 comma 4 comma 7 right curly bracket
  3. left curly bracket 4 comma 7 right curly bracket
  4. left curly bracket 7 right curly bracket

Hint:

In this question we have to find the value of n where f(n) will be greater than 2. From the given function two options will not be considered as in both the cases f(n) will be 2 and o. Now considering the third case we have to find the value of n.

The correct answer is: left curly bracket 1 comma 4 comma 7 right curly bracket


    For f(n)greater than 2n not equal to 3 k space a n d space n not equal to 3 k plus 2
    So, f(n)greater than 2
    we will consider, f(n)=10-n, if n=3k+1
    10 minus n greater than 2
10 minus 2 greater than n
8 greater than n
S o comma space n equals open curly brackets 1 comma 4 comma 7 close curly brackets
open curly brackets n element of N colon f left parenthesis n right parenthesis greater than 2 close curly brackets space equals open curly brackets 1 comma 4 comma 7 close curly brackets

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