How do you find all the values of "a" such that f is continuous on all real numbers?

margbelladot

Find all values of a such that f is continuous on [itex]\Re[/itex]

f(x)= x+1 if x[itex]\leq[/itex] a
x^2 if x>a


I tried solving but i do not even know where to start! Please help!

scurty

We know (or you should know!) that x+1 and x^2 are continuous functions because they are polynomials. When you create a continuous piece-wise function, ##f(x)##, you want ##f(a)## to be continuous. This means ##\displaystyle \lim_{x \to a^-} f(a) = \lim_{x \to a^+} f(a) = f(a)##

You can think of it in lay man's terms as choosing values of a so that you can graph the function without lifting your pencil at ##f(a)##.