Answer:
Step-by-step explanation:
Given
Solving (a): The constants
This implies that:
So, we have:
Factorize:
Expand and Factorize the expression in bracket
Split
Solve for y
The above represents the constants
Solving (b): Increasing values
Here
Follow the same process in (a) but replace all = with >
i.e.
<u>Test the values of each inequality</u>
For ; say
This is true for ; This implies that:
For Say
This is false:
Say i.e.
This is true for . This implies that:
For
implies that:
For say
This is true for . This implies that
We have:
can be combined to give:
So, the interval is:
Solving (c): Decreasing values
Here
i.e.
<u>Test the values of each inequality</u>
For ; say
This is true for ; This implies that:
For ; say
<em>This is false</em>
Say i.e.
This is the same as:
So, we have the interval to be:
For say
This is false
Say i.e
This is also false
So, the intervals are: and .
This can be merged as:
Hence, the interval for is