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JEE Mains · Maths · STD 12 - 1. relation and function
The function \(f : N \to N\) defined by \(f\left( x \right) = x - 5\left[ {\frac{x}{5}} \right]\) , where \(N\) is set of natural numbers and \([x]\) denotes the greatest integer less than or equal to \(x\), is
- A one-one and onto.
- B one-one but not onto.
- C onto but not one-one.
- D neither one-one nor onto
Answer & Solution
Correct Answer
(D) neither one-one nor onto
Step-by-step Solution
Detailed explanation
\(\left. \begin{array}{l} f\left( 1 \right) = 1 - 5\left[ {1/5} \right] = 1\\ f\left( 6 \right) = 6 - 5\left[ {6/5} \right] = 1 \end{array} \right\} \to \) Many one \(f\left( {10} \right) = 10 - 5\left( 2 \right) = 0\) which is not in co-domain. Neither one-one nor onto.
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