Let \(f\) and \(g\) be real functions defines by \(f(x)=\sqrt { x+2 } \)  and \(g\) , then\(g(x)=\sqrt { 4-{ x }^{ 2 } } \) find the following function:  \(f+g\)

Let \(f\) and  \(g\) be real functions defines by \(f(x)=\sqrt { x+2 } \)  and  \(g\) ,then\(g(x)=\sqrt { 4-{ x }^{ 2 } } \) find the following function: f . g

Let \(f\) and  \(g\) be real functions defines by \(f(x)=\sqrt { x+2 } \)  and  \(g\), then\(g(x)=\sqrt { 4-{ x }^{ 2 } } \) find the following function: \(\frac { f }{ g } \)

Find the domain and range of the relation R = {(x, y) : x + y = 8; x, \(y\in N\)}

Let\(f:\left[ 2,\infty \right] \rightarrow R\) and \(g:\left[ -2,\infty \right] \rightarrow R\)  be two real functions defined by \(f(x)=\sqrt { x-2 } \) and \(g(x)=\sqrt { x+2 } \). Find \(f+g\) and \(f-g\)

What are the sum and difference of identity function and the reciprocal function?

Let f(x)=x² and g(x)=2x+1 be two real functions.Find (f + g) (x), (f –g) (x), (fg) (x),\(\left(\frac{f}{g}\right)(x)\)

Let f(x)=x² and g(x)=2x+1 be two real functions.Find (f –g) (x)

Let f(x)=x² and g(x)=2x+1 be two real functions.Find (fg) (x)

If A= {1,2,3), B={1,2,3,4}, C= {5,6} and D={5,6,7,8}, then verify that \((A\times C)\subset (B\times D) \)

Let A and B be two sets such that n(A)=5 and n(B) =2. If a,b,c,d,e are distinct and (a,2),(b,3),(c,2),(d,3),(e,2) are elements of A x B, find A and B.

Let \(f:R\rightarrow R\) and \(g:R\rightarrow R\) defined by  \(f\left( x \right) =x+1\) and\(g\left( x \right) =2x-3\) Find,\(f+g\) , \(f-g\) and \(\frac { f }{ g } \)

Find the values of a and b, if (2a-5,4)=(5,b+6)

Find the values of a and b, if (a-3,b+7)=(3,7)

Which of the following relations are functions?
\( \left\{ (3,3),(4,2),(5,1),(6,0),(7,7) \right\} \)

Which of the following relations are functions?
\(\left\{ (2,0),(4,8),(2,1),(3,6) \right\} \)

Let A = {a,b,c} and B={x: x\( \in \) N, x is a prime number  less than 5}. Find A x B ans B x A.
Show that A x B \( \neq \) B x A.

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 \(={ 2 }^{ n\left( A \right) \times n\left( B \right) }={ 2 }^{ n\left( A\times B \right) }\)

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

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

If \(y=f(x)=\frac { 1-x }{ 1+x } ,\) then show that x = f(y).

Find the range of \(f\left( x \right) =\frac { x-2 }{ 3-x } \)

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).

Let A = {1,2,3,4} and B = {1,4,9,16,25} and R be a relation defined from A to B as \(R=\{ (x,y):x\in A,y\in B,\quad and\quad y={ x }^{ 2 }\} \).
Depict this relation using arrow diagram