Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Given: f ( x ) = { x , 0 ≤ x < 1 2 1 2 , x = 1 2 1 − x , 1 2 < x ≤ 1 f(x) = \begin{cases} x, & 0 \le x < \frac{1}{2} \\ \frac{1}{2}, & x = \frac{1}{2} \\ 1-x, & \frac{1}{2} < x \le 1 \end{cases} f ( x ) = ⎩ ⎨ ⎧ x , 2 1 , 1 − x , 0 ≤ x < 2 1 x = 2 1 2 1 < x ≤ 1
Mathematics
Problem Given: f ( x ) = { x , 0 ≤ x < 1 2 1 2 , x = 1 2 1 − x , 1 2 < x ≤ 1 f(x) = \begin{cases} x, & 0 \le x < \frac{1}{2} \\ \frac{1}{2}, & x = \frac{1}{2} \\ 1-x, & \frac{1}{2} < x \le 1 \end{cases} f ( x ) = ⎩ ⎨ ⎧ x , 2 1 , 1 − x , 0 ≤ x < 2 1 x = 2 1 2 1 < x ≤ 1 g ( x ) = ( x − 1 2 ) 2 g(x) = \left(x - \frac{1}{2}\right)^2 g ( x ) = ( x − 2 1 ) 2 x ∈ R x \in \mathbb{R} x ∈ R y = f ( x ) y = f(x) y = f ( x ) y = g ( x ) y = g(x) y = g ( x ) 2 x = 1 2x = 1 2 x = 1 2 x = 3 2x = \sqrt{3} 2 x = 3 1 3 + 3 4 \frac{1}{3} + \frac{\sqrt{3}}{4} 3 1 + 4 3 3 4 − 1 3 \frac{\sqrt{3}}{4} - \frac{1}{3} 4 3 − 3 1 1 2 + 3 4 \frac{1}{2} + \frac{\sqrt{3}}{4} 2 1 + 4 3 1 2 − 3 4 \frac{1}{2} - \frac{\sqrt{3}}{4} 2 1 − 4 3 Browse the problem library