Answer:
[tex](-9,16][/tex]
Step-by-step explanation:
we know that
The domain of x is equal to the interval--------> [tex](-2,3][/tex]
[tex]-2< x \leq 3[/tex]
All real numbers greater than [tex]-2[/tex] and less than or equal to [tex]3[/tex]
Let
[tex]y=5x+1[/tex]
For [tex]x=3[/tex]
[tex]y=5x+1\\y=5(3)+1=16[/tex]
For [tex]x>-2[/tex]
[tex]y >5(-2)+1\\y > -9[/tex]
so
The range of the function is the interval--------> [tex](-9,16][/tex]
Answer:
(-9,16]
Step-by-step explanation:
It is given that
[tex]-2 < x \le 3[/tex]
We need to find the possible values of [tex]5x+1[/tex].
Multiply all sides by 5 in the above inequality.
[tex]-2\cdot 5 < x\cdot 5 \le 3\cdot 5[/tex]
[tex]-10< 5x\le 15[/tex]
Add 1 on each side.
[tex]-10+1< 5x+1\le 15+1[/tex]
[tex]-9< 5x+1\le 16[/tex]
It is clear that the possible values are lie between -9 and 16 (included).
[tex]5x+1\in (-9,16][/tex]
Close bracket represents that 16 is included in the solution set.
Therefore, the required interval is (-9,16].
