continuity

Consider the function f(t) = (max(0,t))² for -∞ < t < ∞, where max(a, b) denotes the maximum of a and b. Which of the following statements is/are true?

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?

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...

Let $$g\left( x \right) = \left\{ {\matrix{ { - x} & {x \le 1} \cr {x + 1} & {x \ge 1} \cr } } \right.$$ and $$f\left( x \right) = \left\{ {\matrix{ {1 - x,} & {x \le 0} \cr {{x^{2...

Consider the function $$f\left( z \right) = z + {z^ * }$$ where $$z$$ is a complex variable and $${z^ * }$$ denotes its complex conjugate. Which one of the following is TRUE?

At $$t=0,$$ the function $$f\left( t \right) = {{\sin t} \over t}\,\,$$ has