Solution
Solution
+2
Interval Notation
Decimal Notation
Solution steps
Let:
Factor
Apply exponent rule:
Factor out common term
Identify the intervals
Find the signs of the factors of
Find the signs of
Find the signs of
Move to the right side
Add to both sides
Simplify
Move to the right side
Add to both sides
Simplify
Move to the right side
Add to both sides
Simplify
Summarize in a table:
Identify the intervals that satisfy the required condition:
Substitute back
If then
Switch sides
For , if then
Simplify
Use the following trivial identity:
Simplify
Use the following trivial identity:
True for all
Range of
Function range definition
The range of the basic function is
Let
Combine the intervals
Merge Overlapping Intervals
The intersection of two intervals is the set of numbers which are in both intervals
and
Combine the intervals
Merge Overlapping Intervals