JEE Mains · Maths · STD 12 - 1. relation and function
Let \(f, g: N \rightarrow N\) such that \(f(n+1)=f(n)+f(1)\) \(\forall \, n \in N\) and \(g\) be any arbitrary function. Which of the following statements is \(NOT\) true ?
- A If \(fog\) is one-one, then \(g\) is one-one
- B If \(f\) is onto, then \(f ( n )= n\, \forall \,n \in N\)
- C \(f\) is one-one
- D If \(g\) is onto, then \(fog\) is one-one
Answer & Solution
Correct Answer
(D) If \(g\) is onto, then \(fog\) is one-one
Step-by-step Solution
Detailed explanation
\(f(n+1)-f(n)=f(1)\) \(\Rightarrow f(n)=n f(1)\) \(\Rightarrow f\) is one-one Now, Let \(f \left( g \left( x _{2}\right)\right)= f \left( g \left( x _{1}\right)\right)\) \(\Rightarrow g\left(x_{2}\right)=g\left(x_{1}\right)(\) as \(f\) is one-one \()\)…
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