$A$ function $f$ is defined by $f(x) = 2x - 5$. Find the value of $f(-3)$.

Let $f: X \rightarrow Y$ be a function and $A_y = f^{-1}(\{y\})$ for $y \in Y$. Then $A_i \cap A_j = \phi$ $(i \neq j)$ for all $i, j \in Y$ and $\bigcup_{y \in Y} A_y = X$, if

Let $f$ be the subset of $Z \times Z$ defined by $f = \{(ab, a+b) : a, b \in Z\}$. Is $f$ a function from $Z$ to $Z$? Justify your answer.

The function $t$ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t(C) = \frac{9C}{5} + 32$. Find $t(-10)$.

If $f(x) = x^4 - 2x^3 + 3x^2 - ax + b$ is divided by $(x - 1)$ and $(x + 1)$,the remainders are $5$ and $19$,respectively. If $f(x)$ is divided by $(x - 2)$,the remainder is:

The number of relations $R$ from an $m$-element set $A$ to an $n$-element set $B$ satisfying the condition $(a, b_1) \in R, (a, b_2) \in R \Rightarrow b_1 = b_2$ for $a \in A, b_1, b_2 \in B$ is