very basic calculus: f1(x) := max{1, 2-x}, x element of R

[idontknowcookie]

Hi,

f1(x) := max{1, 2-x}, x element of R

What does this mean exactly? Is "2-x" already derived (because of the "max")? What does "1" stand for?

(I have to draw them but I can't when I don't understand what this means.)

Now, I need the domain of definition for:

f1(x) = sin(x), sin^2(x) respectively.

But is it not just R? If I recall correctly, one can put every number for x in the sine-function?!

How do I write the result of the domain of definition in a proper form?

Thank you for your help!

 

[stapel]

f1(x) := max{1, 2-x}, x element of R

What does this mean exactly?

For each x-value, evaluate 2 - x. If the value of 2 - x is less than 1, then use 1, because 1 is the maximum of 1 and 2 - x. But if 2 - x is greater than 1, then use 2 - x.

Now, I need the domain of definition for:

f1(x) = sin(x), sin^2(x) respectively.

I'm sorry, but I don't understand how f₁(x) is equal to these two outputs...?

 

[ksdhart]

Now, I need the domain of definition for:

f1(x) = sin(x), sin^2(x) respectively.

Here, I'm assuming your task was to find the domain of two separate functions, sin(x) and sin^2(x). To find the domain, begin by thinking about what the domain of a function means: Any input which results in a real number output. As you noted the sine function can take any real number as an input, so what do you think the domain is? And since sin^2(x) can be written as sin(x)*sin(x), what do you think the domain of that is?

As for how to write the domain, let's briefly recall the ways in which you can format a domain expression. You could write it in interval notation, like (3, 8], or write it as an inequality, like 3 < x <= 8. Or you could write it like this:

$\displaystyle \left\{x\in \mathbb{Z}\right\}$ (meaning "the set of all x, such that x is an integer")

Any of the above are valid formats, although your teacher/instructor may have one they prefer, in which case you should use that.

 

[idontknowcookie]

For each x-value, evaluate 2 - x. If the value of 2 - x is less than 1, then use 1, because 1 is the maximum of 1 and 2 - x. But if 2 - x is greater than 1, then use 2 - x.


I'm sorry, but I don't understand how f₁(x) is equal to these two outputs...?

Thank you for your reply.

What does "1 is the maximum of 1 and 2 - x" mean? Is 2 - x already derived? I don't really get what the elements mean, especially the "1". Are those specific elements in a set or what?

The sine-questions were a different task, sorry for that.

 

[Ishuda]

Thank you for your reply.

What does "1 is the maximum of 1 and 2 - x" mean? Is 2 - x already derived? I don't really get what the elements mean, especially the "1". Are those specific elements in a set or what?

The sine-questions were a different task, sorry for that.

As stapel said "For each x-value, evaluate 2 - x. ...". So, to find the function value, yes, 2-x is already derived (assuming I understand you correctly). As an example, let x=4, then x-2=2. Since the maximum of 1 and 2 is 2, f1(4)=2. If x=2 then x-2 is equal to 0. Since the maximum of 1 and 0 is 1, f1(2)=1.

In fact, if x is greater than ???, then x-2 is greater than 1 so that for x>???, f1(x)=x-2 and if x is less than or equal to ???, then 1 is greater than or equal to x-2 so that for x$\displaystyle \le$???, f1(x)=1

 

[stapel]

What does "1 is the maximum of 1 and 2 - x" mean? Is 2 - x already derived?

Yes. That's why I said to plug into 2 - x to find the value of 2 - x. Then compare this value to 1.

As for what "1" means, it means "the number one, being one more than zero and one less than two". It's just a counting number. As for "max", it stands for "maximum", which means "the largest or biggest of a set of items". So if x = -3 so 2 - x = 5, then "the maximum of 1 and 5" would be "5'. If x 3 so 2 - x = -1, then "the maximum of 1 and -1" would be 1. That's all there is to this: You plug in, you compare, you pick the bigger one.

Please reply explaining specifically what you don't "get" about this, perhaps showing by example where this isn't making sense for you. Thank you!