How do you algebraicly find the range of a function. I can tell what the range is supposed to be by looking at the graph, but I cannot show it using algebra.
Excellent question. It used to bother me too, until I developed a trick.Originally Posted by redier
Consider a function,
The range are all the values of such that there exists an in the domain such as,
.
---
Example,
Find the range of,
The domain is all real numbers.
Thus, for what values of does the equation have a solution.
Say,
Then,
Thus,
Note this equation can only have a solution when the Left Hand side is non-negative. That is,
.
Thus,
If you solve this inequality (details omitted) you have that,
---
As an excersce,
Find the range of,