Need some explanations

[Fluush]

Hi,
I need some help on this exercise.
Even if it seems not that hard, I mostly don’t understand what I have to do.
Could you help me please ?
Thank you!

 

[Romsek]

Do you know what is meant by the domain of a function?

 

[Fluush]

I'm not sure, I know how to find the domain of a function and graph it thought.
Sorry I'm not sure about all terms in math given that I'm an international student.

 

[Dr.Peterson]

If you don't understand what you are being asked to do, you need to study the topic. If your textbook or class notes do not cover this, search for "piecewise functions". One good starting site is: https://www.mathsisfun.com/sets/functions-piecewise.html

Then give the problem a try so we can see how much you understand.

In general, when you ask for help, it's important not just to tell us what you don't understand, but what you do know, so we can explain in those terms. Please read this.

 

[Steven G]

Hi,
I need some help on this exercise.
Even if it seems not that hard, I mostly don’t understand what I have to do.
Could you help me please ?
Thank you!

I'll give it a try.
f(x) has two rules. One is 2x-3 and the other rule is 3x-5.

A great question to ask is how do we know which rule to use. The answer is quite simply, only use 2x-3 if -5< x < -1
And use 3x-5 only if x>1.

For example find f(7). 1st decide if 7 is between -5 and -1 OR if 7>1. Since 7>1 we will use the rule 3x-5. So f(7) = 3(7)-5 =21-5=16.
Another example is to find f(-2). Since -2 is between -5 and -1, we use the rule 2x-3. So f(-2) = 2(-2)-3 = -4-3=-7.

What about f(1/2). Now 1/2 is NOT between -5 and -1 AND 1/2 is not greater than 1. So we have no definition for x=1/2.

When we do have a definition for some x-value, we say that x-value is in the domain of f(x) or simply in the domain.
If we do not have a definition for some x-value, we say that x-value is NOT in the domain of f(x)