If a real-valued function $f:[a, \infty) \rightarrow [b, \infty)$ defined by $f(x) = 2x^2 - 3x + 5$ is a bijection,then $3a + 2b =$

The function $f: N \rightarrow Z$ defined by $f(n) = \begin{cases} \frac{n}{2} & , n \text{ is even} \\ -\left(\frac{n-1}{2}\right) & , n \text{ is odd} \end{cases}$ is . . . . . . .

If $f: N \rightarrow R$ is defined by $f(1)=-1$ and $f(n+1)=3f(n)+2$ for $n \geq 1$, then $f$ is

For each $n \in N$, let $A_n = \{(n+1)k \mid k \in N\}$ and $X = \bigcup_{n \in N} A_n$. $A$ mapping $f: X \rightarrow N$ defined by $f(x) = x, \forall x \in X$, is

The function $f: R-\{1\} \rightarrow R-\{4\}$ defined by $f(x) = \frac{4x-3}{x-1}$ for $x \in R-\{1\}$ is

Consider the function $f(x) = x^3 - 8x^2 + 20x - 13$. The function $f: R \rightarrow R$ is: