If f(x) = x³ -\(1\over x^3\) ,Then find f(x) + f\(({1\over x})\) = 0

If f(x) = x²- 3x + 4, find values of x satisfying f(x) = f(2x + 1).

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

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(0)

Let R be a relation on the set Z of integers defined by R = {(x, y) : x, y \(\in\) Z, x² + y² = 25} Find R in roster form

Let R be a relation on set N of natural numbers defined by R = {(x, y) : x, y\(\in\)N, x + 3y = 12} Find Range of R

Let R be a relation on set N of natural numbers defined by R = {(x, y) : x, y\(\in\)N, x + 3y = 12} Find Domain of R

Find the inverse relation \(\left( { R }^{ -1 } \right) \)in each of the following cases R= {(x,y) : x, y \(\in\) N, x + 2y = 8}

Find the inverse relation \(\left( { R }^{ -1 } \right) \)in each of the following cases R = {(1,2),(1,3),(2,3),(3,2),(5,6)}

If A x B = {a,1), (b,3), (a,3), (b,1), (a,2), (b,2)}. Then, find A and B.

If two functions are defined as \(f(x)=\frac { 1 }{ (x-2) } ,x\neq 2\) and \(g(x)=(x-2)^{ 2 }\) then find  \(\frac { f }{ g } \)

If A = {1,2}, then find A x A x A

If n(A) = 3 and B = {2,3,4,6,7,8}, then find the number of relations from A to B.

If A = {a,b} and B = {2,3}, then find the number of relations from A to B.
Number of relations from A to B \(={ 2 }^{ n\left( A \right) \times n\left( B \right) }={ 2 }^{ n\left( A\times B \right) }\)