Easy way to find the number of roots of a function

Question

I want to know if there is an easy way to find the number of roots in a function. For example let's consider the function:

$\\f(x) = \sqrt{25-x^2}-e^{|x|}$

How many solutions does the $f(x) = 0$ equation have?

Answer 1

Generally, you need to have some intuition about the shapes of the functions. The first half of your function is a circle, and the last half is something that sort of looks like a parabola. You then consider how many ways that pseudo-parabola can intersect with the circle. In this case, it should be two.