Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Consider the function f(x) = cases x - [x] - 1 2 , & if x I 0, & if x I cases
MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration
Problem Consider the functionf ( x ) = { x − [ x ] − 1 2 , if x ∉ I 0 , if x ∈ I , where [ . ] denotes the greatest integer function and I is the set of integers. f(x) = \begin{cases} x - [x] - \frac{1}{2}, & \text{if } x \notin I \\ 0, & \text{if } x \in I \end{cases}, \text{ where } [.] \text{ denotes the greatest integer function and } I \text{ is the set of integers.} f ( x ) = { x − [ x ] − 2 1 , 0 , if x ∈ / I if x ∈ I , where [ . ] denotes the greatest integer function and I is the set of integers. g ( x ) = max { x 2 , f ( x ) , ∣ x ∣ } g(x) = \max \{x^2, f(x), |x|\} g ( x ) = max { x 2 , f ( x ) , ∣ x ∣ } − 2 ≤ x ≤ 2 -2 \le x \le 2 − 2 ≤ x ≤ 2 g ( x ) g(x) g ( x ) − 2 ≤ x ≤ 2 -2 \le x \le 2 − 2 ≤ x ≤ 2 Browse the problem library