Let $A = \{0, 1, 2, 3, 4, 5, 6, 7\}$. Then the number of bijective functions $f: A \rightarrow A$ such that $f(1) + f(2) = 3 - f(3)$ is equal to $.....$

The function $f(x) = \frac{x^2+2x-15}{x^2-4x+9}$,$x \in R$ is

In each of the following cases,state whether the function is one-one,onto or bijective. Justify your answer. $f : R \rightarrow R$ defined by $f(x) = 1 + x^2$.

Let $f, g: N - \{1\} \rightarrow N$ be functions defined by $f(a) = \alpha$,where $\alpha$ is the maximum of the powers of those primes $p$ such that $p^{\alpha}$ divides $a$,and $g(a) = a + 1$,for all $a \in N - \{1\}$. Then,the function $f + g$ is.

On the set of integers $Z$,define $f: Z \rightarrow Z$ as $f(n) = \begin{cases} \frac{n}{2}, & n \text{ is even} \\ 0, & n \text{ is odd} \end{cases}$. Then $f$ is:

Let $f, g: N \rightarrow N$ such that $f(n+1)=f(n)+f(1)$ for all $n \in N$ and $g$ be any arbitrary function. Which of the following statements is $NOT$ true?