The function $t$,which maps temperature in degree Celsius into temperature in degree Fahrenheit,is defined by $t(C) = \frac{9C}{5} + 32$. Find the value of $C$ when $t(C) = 212$.

The relation $f$ is defined by $f(x) = \begin{cases} x^2, & 0 \le x \le 3 \\ 3x, & 3 \le x \le 10 \end{cases}$. The relation $g$ is defined by $g(x) = \begin{cases} x^2, & 0 \le x \le 2 \\ 3x, & 2 \le x \le 10 \end{cases}$. Show that $f$ is a function and $g$ is not a function.

Examine the following relation and state whether it is a function or not,giving reasons:
$R = \{(2, 1), (3, 1), (4, 2)\}$

Which of the following relations are functions? Give reasons. If it is a function,determine its domain and range.
$\{(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)\}$

$A$ function $f$ is defined by $f(x) = 2x - 5$. Find the values of $f(0)$,$f(7)$,and $f(-3)$.

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