Find k, if f(k) = 2k - 1 and f o f(k) = 5.

Let A =  {1,2, 3, 4} and B = {-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Let R = {(1, 3), (2, 6), (3, 10), (4, 9)} \(\subseteq \) A x B be a relation. Show that R is a function and find its domain, co-domain and the range of R.

Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as  a set of ordered pairs.

State whether the graph represent a function. Use vertical line test.

If the Set 'A' has 3 elements. and the Set B {3, 4, 5}, find the number of elements in (A x B).

If G = {7,8} and H = {5,4,2} find, G x H and H x G.

\(\text { If } \mathrm{A}=\{-1,1\}, \text { find } \mathrm{A} \times \mathbf{A} \times \mathbf{A}\)

If A x B = {(a, x), (a, y), (b, x), (b, y)}, find 'A' and 'B'.

Let A = {3, 5} and B = {7,11} Let R, = {(a, b); a \(\in\) A, b \(\in\) B, a - b is odd}. Show that R is an empty relation from A into B.

What is the number of relations on A if R is a relation on a finite set A having 'n' elements?

Let set A = {January, February, April, June, September, October, November, December) and set B = {28, 29, 30, 31}. Let R be a relation  from A to B defined by R = {(a, b) \(\in\) A x B : 'a' month has 'b' number of days}. Write a subset of relation R connected with 'Teachers Day'.

A function 'f' is defined by f (x) = 2x- 5. write down the values of f (0), f(7) and f(- 3).

If A - {1,2,3} and B = {a, b, c} then do 
i) {(1, a), (2,b), (2, c), (3, c)} and
ii) {(2, b), (3, b)} represent a function A \(\rightarrow\) B?

Let A = {1,2,3} and B = {4,5} Let R = {(1,4),(1, 5), (2,4), (3, 5)}. Is 'f' a function from A into B?

Find the domain of \(f(x)=\frac{x}{x^{2}-5 x+6}\)