If f and g be two real function defined by \(f\left( x \right) =\sqrt { x+1 } \)and \(g\left( x \right) =\sqrt { 9-{ x }^{ 2 } } \) .Then, describe each of the following functions.  \(\frac { f }{ g } \)

If X = {1, 2, 3, 4, 5}, Y = {1, 2, 5, 6, 7, 9, 10, 11, 12, 13, 14} and \(f:X\rightarrow Y\) be defined by f(x) = 2x+3, then find the domainand range of f.

If A = {a,d}, B = {b,c,e} and C = {b,c,f}, then verify that \(A\times (B\cup C)=(A\times B)\cup (A\times C)\)

Find the domain of the function f defined by \(f(x)=\sqrt { 4-x } +\frac { 1 }{ \sqrt { { x }^{ 2 }-1 } } \)

If a function \(f:R\rightarrow R\)  be defined by
\(f(x)=\begin{cases} 3x-2,\quad x<0 \\ 1,\quad \quad \quad \quad x=0 \\ 4x+1,\quad x>0 \end{cases}\)
Find f(1), f(-1), f(0), f(2).

Determine the domain and range of the relation defined as: R = {(a, b) : a, b\(\in\)N, a < 5, b = 3a + 1}

Let A= {x, y} and B = {a, b}, How many relations are there from A to B. Write all the relations

Find the domain and range of the following real functions  \(f(x)=\sqrt{9-x^2}\)

The relation f is defined by 
\(f(x)=\begin{cases} { x }^{ 2 },\quad 0\le x \le 3 \\ 3x,\quad3\le x<10\end{cases}\)
The relation g is defined by
\(g(x)=\begin{cases} { x }^{ 2 },\quad 0\le x \le 2 \\ 3x,\quad2\le x\le10\end{cases}\)
Show that f is a function and g is not a function.

If A \(\subset\) B then prove that A x A = (A x B) \(\cap\) (B x A).

If A and B are any two non-empty sets, then prove that A x B = B x A \(\Leftrightarrow \) A = B