Let R be a relation from a set A to B, then ______.

If R is a relation from a finite set A having m elements to a finite set B having n elemen.ts, then the number of relations from A to B is ______.

If \(f(x)={2^x+2^{-x}\over 2}\) then f(x+y) f(x-y)is equal to ______.

If f(x) =\({x+1\over x-1}\) is a real function,\(\neq\) 1, then \(f[f\{f(2)\}]\) is ______.

The domain of the function \(f(x)=\sqrt{x-1}+\sqrt{3-x}\) is ______.

Let A = {1, 2, 3}, B = {2, 3, 4, 5}, state as to which of the following sets R represents a relation of set A into set B?
If R represents a relation, write its domain and range.
R = {(2, 1), (1, 3), (4, 3)}

Let A = {1, 2, 3}, B = {2, 3, 4, 5}, state as to which of the following sets R represents a relation of set A into set B?
If R represents a relation, write its domain and range.
R = {(1, 2), (2, 3), (3, 4), (3, 2)}

Which of the following relations are functions? Give reasons if it is a function, and determine the domain and range{(4, 1), (6, 2), (8, 3), (10, 4), (12, 5)}

Which of the following relations are functions? Give reasons if it is a function, and determine the domain and range {(3, 10), (5, 12), (7, 14), (5, 16)}

Find x and y when (3x + 2y, x + 4y - 1) = (6, 6).

Find the domain and range of the following functions: f(x) =\({|x-3|\over x-3},x\in R\)

A function f: R \(\rightarrow\)R is defined as
\(f(x)=\begin{cases} x^2+1\quad x\le-2 \\ 2x+1 \quad -2<x\le3\\ 2x^3-3\quad 3<x<8 \end{cases}\)
Find f(3)

A function f: R \(\rightarrow\)R is defined as
\(f(x)=\begin{cases} x^2+1\quad x\le-2 \\ 2x+1 \quad -2<x\le3\\ 2x^3-3\quad 3<x<8 \end{cases}\)
Find f(-3)

Determine the domain and range of the relation: R = {(x, x²): x is prime, 10\(\le\) x \(\le\) 30}.

Determine the range and domain of the relation: R = {(x, y): y = I x + 1|, x \(\in\) Z, IxI \(\le\)3}.

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. f+g

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

Let A, B, C and D be any non-empty sets.
Prove that (A xB)\(\cap\)(CxD) =(A\(\cap\)C) x (B\(\cap\)D).

If R is the relation "less than" from A ={1,2, 3, 4, 5} to B = {1, 4, 5}. Write down the set of ordered pairs corresponding to R. Find the inverse of R.