If f - N - Z is defined by fn - - n - 1-2- when n is odd- - n-2- when n is even - then identify the type of function-

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Proof by mathematical induction

If f : N → ...

Question

If $f : N \to Z$ is defined by $f (n) = {\begin{matrix} \frac{n - 1}{2}, & w h e n n i s o d d - \frac{n}{2}, & w h e n n i s e v e n \end{matrix}$ then identify the type of function.

Open in App

Solution

Suggest Corrections

Similar questions

$i f f : N \to N i s d e f i n e d b y f (n) = n - (- 1)^{n}, t h e n$

Let $f : N \to N$ be defined by $f (n) = {\begin{matrix} \frac{n + 1}{2}, if n is odd \frac{n}{2}, if n is even \end{matrix}}$ for all $n \in N$ .

State whether the function $f$ is bijective. Justify your answer.

f : N \to N

N

f (n) = 2 n + 3

f : N \to N

f

f : Z \to Z, f (n) = {\begin{matrix} \frac{n}{2} : n is even \frac{- n + 1}{2} : n is odd \end{matrix}

f

Join BYJU'S Learning Program