Modulus Function or Absolute Value Function
Functions of Class 11
Modulus Function or Absolute Value Function
y = |x| = x, x ≥ 0
= - x, x < 0
Properties of modulus function
(a) |x| ≤ a ⇒ -a ≤ x ≤ a a ≥ 0
(b) |x| ≥ a ⇒ x ≤ -a or x ≥ a a ≥ 0
(c) |x+y| = |x| + |y| ⇔ x ≥ 0 y ≥ 0
or x ≤ 0 y ≤ 0
(d) |x-y| = |x| - |y| ⇒ x ≥ 0 and |x| ≥ |y|
Or x ≤ 0 and y ≤ 0 and |x| ≥ |y|
(e) |x ± y| ≤ |x| + |y|
(f) |x ± y| ≥ | |x| - |y| |
- Introduction
- Algebraic Operations On Functions
- Type of Functions
- Composition of functions
- Invertible Functions
- Domain and Range of Inverse Trigonometric Functions
- Odd And Even Functions
- Periodic Functions
- Methods to Find Period of A Periodic Function
- Signum Function
- Greatest Integer Function
- Modulus Function or Absolute Value Function
- Rational And Irrational Function
- Algebraic And Transcendental Function
- Explicit Function
- Exercise 1
- Exercise 3(Subjective)
