Let x ∈ R. A function f(x) = [x] defined as f(x) = n (n is an integer) such that n ≤ x < n + 1 is called a step function.
For all x such that 0 ≤ x < 1
f(x) = 0
For all x such that -1 ≤ x < 0
f(x) = -1
- 2 ≤ x < 1
f(x) = -2 etc.,
Domain of f = R
Range of f = Z
If f(x) = [x + k] = [x] + k where k is an integer
Example 1:
Solution set of [x] = -2 is { x | -2 ≤ x < -1}
Example 2:
f: Z→Z defined by f(x) = [x] is one–one and onto.
f: R→Z defined by f(x) = [x] is onto but
not one–one.
f: Z→R defined by f(x) = [x] is one–one
but not onto.
f: R→R defined by f(x) = [x] is neither one–one
nor onto.
Try this question
- Identify this type of function
a. |
|
Solution:
a. Step function |