11th Mathematics NCERT Chapter 2
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– Relations and Functions:
– Summary: This chapter covers the concepts of relations and functions, defining ordered pairs, Cartesian products, relation, domain, range, and functions. It also delves into real-valued functions, polynomial functions, and various types of functions like identity functions, constant functions, and modulus functions【4:4†source】.
– Polynomial Functions: It defines polynomial functions as functions that can be written in the form f(x) = a0 + a1x + a2x^2 + … + anx^n, with examples and discussions on domains, ranges, and graphical representations【4:4†source】.
– Algebra of Real Functions: Explains the addition, subtraction, multiplication, and division of real functions along with scalar multiplication. Provides examples for better understanding【4:2†source】.
– Identity Function: Defined as f(x) = x for all x belonging to the set of real numbers. The domain and range of the identity function are the set of real numbers. The graph is a straight line passing through the origin【4:2†source】.
– Constant Function: Defined as f(x) = c for all x belonging to the set of real numbers where c is a constant. The domain of a constant function is the set of real numbers and its range is a singleton set {c}【4:2†source】.
Define a relation R from A to A by R = {(x, y) : 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain, and range.
Find the number of relations from set A = {1, 2} to set B = {3, 4}.
Show that f is a function and g is not a function based on their definitions.
If f(x) = x^2, find (1, 1) – f .
Find the domain and the range of the real function f defined by f(x) = -1*x.
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