The range of the function $g(x) = \frac{2}{2+4x^2}$ can be written as an interval $(a,b]$. What is $a+b$?

powclaire Feb 16, 2021

#1**+2 **

Let's find the lowest \(2+4x^2\) can be and the highest.

The lowest is when x = 0, and the value of the fraction is 1. When the value of the denominator is the lowest, the value of the fracture is highest (I hope that makes sense) so the highest value of the fraction is 1. (So b = 1)

The highest is .... well, there is no highest. However, no matter how high the denominator is, 2/(big number) the fraction will never be 0. So a = 0.

We have a = 0, and b = 1, so the sum is 1.

Guest Feb 16, 2021