Let denote the set of all natural numbers, and denote the set of all integers. Consider…
Mathematics · JEE Advanced · NTA Exams — Sets, Relations and Functions
Let 
denote the set of all natural numbers, and 
denote the set of all integers. Consider the functions 
defined by
\(\ ext { and } g(n)=\left\{\begin{array}{cc} 3+2 n & \ ext { if } n \geq 0 \\ -2 n & \ ext { if } n<0 \end{array}\right.\).
Define (gof )(n) = g(f(n)) for all \(n \in \mathbb{N},\) and
(fog) (n) = f(g(n)) for all
Then which of the following statements is (are) TRUE?
denote the set of all natural numbers, and denote the set of all integers. Consider the functions defined by \(\ ext { and } g(n)=\left\{\begin{array}{cc} 3+2 n & \ ext { if } n \geq 0 \\ -2 n & \ ext { if } n<0 \end{array}\right.\).
Define (gof )(n) = g(f(n)) for all \(n \in \mathbb{N},\) and
(fog) (n) = f(g(n)) for all
Then which of the following statements is (are) TRUE?
- gof is NOT one-one and gof is NOT onto
- fog is NOT one-one and fog is onto
- g is one-one and g is onto
- f is NOT one-one but f is onto
Answer
(A) gof is NOT one-one and gof is NOT onto
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