piecewise function

Consider ordinary differential equations given by ẋ₁(t) = 2x₂(t) ẋ₂(t) = r(t) with initial conditions x₁(0) = 1 and x₂(0) = 0. If r(t) = {1, t ≥ 0; 0, t < 0}, then at t = 1, x₁(t)...

Consider the function $f(t) = (\text{max}(0,t))^2$ for $- \infty

Let f be a real-valued function of a real variable defined as f(x) = x² for x\ge0, and f(x) = -x² for x<0. Which one of the following statements is true?

Let g(x) = { -x, x ≤ 1 and f(x) = { 1-x, x ≤ 0 x+1, x ≥ 1 x², x > 0 Consider the composition of f and g, i.e., (f∘g)(x) = f(g(x)). The number of discontinuities in (f∘g)(x) present...

A function $f(x)$ is defined as $f(x)=\begin{cases} e^x, & x<1 \ \ln x+ax^2+bx, & x\ge1 \end{cases}$, where $x \in \mathbb{R}$. Which one of the following statements is TRUE?

A function $$f(x)$$ is defined as $$f\left( x \right) = \left\{ {\matrix{ {{e^x},x < 1} \cr {\ln x + a{x^2} + bx,x \ge 1} \cr } \,\,,\,\,} \right.$$ where $$x \in R.$$ Which one of...