1,000,000 Question Thread :D

[crappy]

dom g o f is the dom of f
so is the ran g o f the ran of f?

No

[TrueTears]

dom g o f is the dom of f
so is the ran g o f the ran of f?

No you must work it out manually.

EDIT: beaten by crappy xD

[/0]

If you have and

Then the range of will not be the same as the range of

In general you have to look at the whole composite function within its domain to find the range. Sometimes it can be quite hard, but it helps to have a knowledge of what the ranges of different types of graphs are.

[kenhung123]

If you have and

Then the range of will not be the same as the range of

In general you have to look at the whole composite function within its domain to find the range. Sometimes it can be quite hard, but it helps to have a knowledge of what the ranges of different types of graphs are.

You don't simply just substitute the largest and smallest value of the dom of f into the composite function to find the range right? So we just need to visualise the composite graph.

[/0]

Yeah, subbing in the endpoints is generally not safe unless you are sure the graph is increasing or decreasing for all x in the domain. It is useful to be able to visualise the graph.

[TrueTears]

Always sketch the graph just to make sure.

[kenhung123]

Thank you for your consistent help.

[kenhung123]

Can someone explain the modulus meaning, purpose and steps to tackle as they would to a 5 year old?

[TrueTears]

Can someone explain the modulus meaning, purpose and steps to tackle as they would to a 5 year old?

Not to be unhelpful or anything but just wondering have you read the chapter on modulus function in Essentials 3/4 CAS book? I found that Essentials explained modulus functions very very well.

[kenhung123]

Can someone explain the modulus meaning, purpose and steps to tackle as they would to a 5 year old?

Not to be unhelpful or anything but just wondering have you read the chapter on modulus function in Essentials 3/4 CAS book? I found that Essentials explained modulus functions very very well.

Thanks very much! It is very useful. I found that they had |x|=x^(1/2), does that mean the result must always be positive?

[TrueTears]

Can someone explain the modulus meaning, purpose and steps to tackle as they would to a 5 year old?

Not to be unhelpful or anything but just wondering have you read the chapter on modulus function in Essentials 3/4 CAS book? I found that Essentials explained modulus functions very very well.

Thanks very much! It is very useful. I found that they had |x|=x^(1/2), does that mean the result must always be positive?

Just to clarify some things:



So yes whatever you plug into must come out to be positive.

[kenhung123]

Oh ok. Why is it that when we solve for 0 we get the point which the x value turn <0?
E.g. |x-4|, x=4

[TrueTears]

Oh ok. Why is it that when we solve for 0 we get the point which the x value turn <0?
E.g. |x-4|, x=4

I'm not sure what you mean, just follow the conventional splitting up cases method if you want to do it algebraically.



Case 1:





Case 2:





Overall

[kenhung123]

(|x|)^2=?

[TrueTears]

Can someone explain the modulus meaning, purpose and steps to tackle as they would to a 5 year old?

Not to be unhelpful or anything but just wondering have you read the chapter on modulus function in Essentials 3/4 CAS book? I found that Essentials explained modulus functions very very well.

Thanks very much! It is very useful. I found that they had |x|=x^(1/2), does that mean the result must always be positive?

Just to clarify some things:



So yes whatever you plug into must come out to be positive.