Define a function as a set of ordered pairs.

Define a function as a correspondence between two sets.

What is the fundamental difference between a relation and function? Is every relation a function?

Let X = {1, 2, 3, 4,}, Y = {1, 5, 9, 11, 15, 16} and F = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}.

Are the following true?

(i) F is a relation from X to Y (ii) F is a function from X to Y. Justify your answer in following true?

Let X = {-1, 0, 3, 7, 9} and f : X → R : f(x) x³ + 1. Express the function f as set of ordered pairs.

Let A = {–1, 0, 1, 2} and B = {2, 3, 4, 5}. Find which of the following are function from A to B. Give reason.

(i) f = {(–1, 2), (-1, 3), (0, 4), 1,5)}

(ii) g = {(0, 2), (1, 3), (2, 4)}

(iii) h = {(-1, 2), (0, 3), (1, 4), (2, 5)}

Let A = {1, 2} and B = {2, 4, 6}. Let f = {(x, y) : x ϵ A, y ϵ B and y > 2x + 1}. Write f as a set of ordered pairs. Show that f is a relation but not a function from A to B.

Let A = {0, 1, 2} and B = {3, 5, 7, 9}. Let f = {(x, y) : x ϵ A, y ϵ B and y = 2x + 3}. Write f as a set of ordered pairs. Show that f is function from A to B. Find dom (f) and range (f).

Let A = {2, 3, 5, 7} and B = {3, 5, 9, 13, 15}. Let f = {(x, y) : x ϵ A, y ϵ B and y = 2x – 1}. Write f in roster form. Show that f is a function from A to B. Find the domain and range of f.

Let g = {(1, 2), (2, 5), (3, 8), (4, 10), (5, 12), (6, 12)}. Is g a function? If yes, its domain range. If no, give reason.

Let f = {(0, -5), (1, -2), (3, 4), (4, 7)} be a linear function from Z into Z. Write an expression for f.

If f(x) = x², find the value of .

Let X = {12, 13, 14, 15, 16, 17} and f : A → Z : f(x) = highest prime factor of x. Find range (f)

Let R⁺ be the set of all positive real numbers. Let f : R⁺→ R : f(x) = log_ex. Find

(i) range (f)

(ii) {x : x ϵ R⁺ and f(x) = -2}.

(iii) Find out whether f(x + y) = f(x). f(y) for all x, y ϵ R.

Let f : R → R : f(x) =2^x. Find

(i) range (f)

(ii) {x : f(x) = 1}.

(iii) Find out whether f(x + y) = f(x). f(y) for all x, y ϵ R.

Let f : R → R : f(x) =x² and g : C → C: g(x) =x², where C is the set of all complex numbers. Show that f ≠ g.

f, g and h are three functions defined from R to R as following:

(i) f(x) = x²

(ii) g(x) = x² + 1

(iii) h(x) = sin x

That, find the range of each function.

Let f : R → R : f(x) = x² + 1. Find

(i) f^–1 {10}

(ii) f^–1 {–3}.

The function is the formula to convert x °C to Fahrenheit units. Find

(i) F(0),

(ii) F(–10),

(iii) The value of x when f(x) = 212.

Interpret the result in each case.