Properties of Modulus Function
The properties of modulus functions are listed below:
Inequalities Property
- If a > 0, |x| < a ⇒ -a < x < a
- If a > 0, |x| > a ⇒ x ∈ (-∞, -a) ∪ (a, ∞)
- If a < 0, |x| > a is valid for all real numbers.
If a and b are Two Real Numbers
- |-a| = a
- |a – b| = 0 ⇔ a = b
- |a + b| ≤ |a| + |b|
- |a – b| ≥ |a| – |b|
- |ab| = |a| |b|
- |a / b| = |a| / |b|, b≠ 0
Modulus Function
Modulus function gives the absolute value or magnitude of a number irrespective of the number is positive or negative. The modulus function is denoted as y = |x| or f(x) = |x|, where f: R→ [0, ∞) and x ∈ R. In this article we will explore modulus function, modulus function formula domain and range of modulus function, modulus function graph, modulus function properties. We will also discuss the application of modulus function and derivative and integral of modulus function. Let’s start our learning on the topic “Modulus Function”.