Mathematics OpenStudy (anonymous):

How do you find the domain of f(r,s)=sqrt(1-r)-e^(r/s)? OpenStudy (anonymous):

$f(r,s)=\sqrt{1-r}-e^{r/s}$ correct? OpenStudy (anonymous):

yes OpenStudy (anonymous):

Okay, what's the domain of the square root function? Given $$f(x)=\sqrt x$$, clearly, the domain is $$x\ge0$$, right? How would this translate to your function? OpenStudy (anonymous):

For the first term, that is. OpenStudy (anonymous):

r cannot be greater than one? OpenStudy (anonymous):

Right! Now onto the next term. What do you know about the exponential function, $$f(x)=e^x$$ ? What's the domain here, in terms of $$x$$? OpenStudy (anonymous):

all real numbers? OpenStudy (anonymous):

Right again! However, the exponent isn't just $$x$$, or $$r$$ or $$s$$. Since it's $$\dfrac{r}{s}$$, you have to correct for this. What values of $$r$$ or $$s$$ can't be used here? OpenStudy (anonymous):

well, r can be anything...even zero. but s can't be zero? OpenStudy (anonymous):

Yes. So what would the overall domain of $$f(r,s)$$ be? OpenStudy (anonymous):

$s \neq 0$and$r \ge 1$but is there a certain way that it needs to be formatted to be "correct?" OpenStudy (anonymous):

Correct! There are a few ways of writing the domain set, but here's one of the more common forms for 2-variable functions like this one: $f(x)=\left\{(r,s)\in\mathbb{R}^2~|~r\ge1,~s\not=0\right\}$ Which would translate, roughly, to "the set of all coordinate points in the x-y (r-s, or real) plane such that r is at least 1 and s is non-zero." OpenStudy (anonymous):

okay, thank you so much! OpenStudy (anonymous):

You're welcome!

Latest Questions bruhbruh2003: Read the sentence. Margot prefers the action of a hockey game to watching ice skating performances.
8 hours ago 3 Replies 0 Medals karremat: can someone pls check this website and see if it needs anything or its perfesct
1 minute ago 6 Replies 0 Medals nagelrdksojro: Polygon ABCD has sides with these lengths: , 5 units; , 4 units; , 4.5 units; and , 7 units.
10 hours ago 4 Replies 3 Medals chels0987: Where should a pronoun be placed?
11 hours ago 2 Replies 2 Medals chels0987: Identify the method used to correct the ambiguous pronoun reference. If the revised sentence does not improve the pronoun reference, choose "No improvement
11 hours ago 1 Reply 0 Medals ghostly111: does anyone know how to create grup chats on here?
15 hours ago 7 Replies 2 Medals jowhite: An elephantu2019s heart rate was measured at 26 beats in 1 minute. If the heart rate remains the same, how many times would the elephantu2019s heart beat in
16 hours ago 3 Replies 1 Medal karremat: Hi I just need someone to check if my info graphic is good
17 hours ago 12 Replies 0 Medals jowhite: In which example is no work done on an object? A. pushing against a sturdy brick wall B.
17 hours ago 10 Replies 4 Medals DustinSettle: Juan runs a company that makes pens. He notices that 1 out of every 9 pens are faulty.
18 hours ago 1 Reply 4 Medals