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 function $t$ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t(C) = \frac{9C}{5} + 32$. Find $t(0)$.

Let $N$ be the set of natural numbers. Define a function $f: N \rightarrow N$ by $f(x) = 2x + 1$. Using this definition,complete the table given below.

$x$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$y$	$f(1) = \dots$	$f(2) = \dots$	$f(3) = \dots$	$f(4) = \dots$	$f(5) = \dots$	$f(6) = \dots$	$f(7) = \dots$

If $Q$ denotes the set of all rational numbers and $f\left(\frac{p}{q}\right)=\sqrt{p^2-q^2}$ for any $\frac{p}{q} \in Q$, then observe the following statements.
$I$. $f\left(\frac{p}{q}\right)$ is real for each $\frac{p}{q} \in Q$.
$II$. $f\left(\frac{p}{q}\right)$ is a complex number for each $\frac{p}{q} \in Q$.
Which of the following is correct?

Let $f: R \rightarrow R$ be defined by $f(x)=x^2+1$. Then,the pre-images of $17$ and $-3$ respectively are

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: