A relation ‘f’ \(X \rightarrow Y\) is defined by f(x) = x² - 2 where x \(\in \) {-2, -1, 0, 3} and Y = R
(i) List the elements of f
(ii) Is f a function?

If X = {–5, 1, 3, 4} and Y = {a, b, c}, then which of the following relations are functions from X to Y ?
R₁= {(–5, a), (1, a), (3, b)}

Given f(x) = 2x - x², find
(i) f (1)
(ii) f (x + 1)
(iii) f (x) + f (1)

Find f o g and g o f when f(x) = 2x + 1 and g(x) = x² - 2

Represent the function f(x) =\(\sqrt { 2x^{ 2 }-5x+3 } \) as a composition of two functions.

If f(x) = 3x - 2, g(x) = 2x + k and if f o g = f o f, then find the value of k..

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

If f(x) = 2x + 3, g(x) = 1 - 2x and h(x) = 3x. Prove that f o(g o h) = (f o g) o h.

Find x if gff(x) = fgg(x), given f(x) = 3x + 1 and g(x) = x + 3.

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 bea 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.

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

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 an arrow .

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