The arrow diagram shows a relationship between the sets P and Q. Write the relation in
(i) Set builder form
(ii) Roster form
(iii) What is the domain and range of R.

Let A = {1,2,3}, B = {4, 5, 6,7}, and f = {(1, 4),(2, 5),(3, 6)}  be a function from A to B. Show that f is one – one but not onto function.

If A = {-2, -1, 0, 1, 2} and f: A ⟶ B is an onto function defined by f(x) = x² + x + 1 then find B.

If the function f: R⟶ R defined by 
\(f(x)=\left\{\begin{array}{l} 2 x+7, x<-2 \\ x^{2}-2,-2 \leq x<3 \\ 3 x-2, x \geq 3 \end{array}\right.\)
(i) f( 4)
(ii) f( -2)
(iii) f(4) + 2f(1)
(iv) \(\frac { f(1)-3f(4) }{ f(-3) } \)

Let f = {(2, 7); (3, 4), (7, 9), (-1, 6), (0, 2), (5,3)} be a function from A = {-1,0, 2, 3, 5, 7} to B = {2, 3, 4, 6, 7, 9}. Is this
(i) an one-one function
(ii) an onto function,
(iii) both one and onto function?

A function f: [-7,6) \(\rightarrow\) R is defined as follows.

find 2f(-4) + 3f(2)

A function f: [-7,6) \(\rightarrow\) R is defined as follows.

f(-7) - f(-3)

A function f: [-7,6) \(\rightarrow\) R is defined as follows.

\(\cfrac { 4f(-3)+2f(4) }{ f(-6)-3f(1) } \)

f(x) = (1+ x)
g(x) = (2x - 1)
Show that fo(g(x)) = gof(x)

Let A = {1, 2, 3, 4, 5}, B = N and f: A \(\rightarrow\)B be defined by f(x) = x². Find the range of f. Identify the type of function.