Domain of combinations?? (emergency)
- Thread starter supehr
- Start date
Hello!
I really need help with these domain questions ASAP. I've added the answer I thought it's supposed to be but apparently i'm wrong!
Hi,Remember that the domain of the two functions has to satisfy (be a subset of) the domains of the individual functions. For example take the f-g question
f(x) = \(\displaystyle \sqrt{5-x},\, x\, \epsilon\, (-\infty,\, 5]\)
g(x) = \(\displaystyle \sqrt{x^2-4},\, x\, \epsilon\, (-\infty,\, 2]\, or\, x\, \epsilon\, [2, \, \infty)\)
Now we take the two segment of g(x) separately. For the left hand segment, x must be less than or equal to 2. That will satisfy f(x), so we can use the complete left hand segment for f-g. For the right hand segment, x must be greater than or equal to 2 but f(x) says we must also be less than or equal to 5. So, to satisfy both, the right hand segment must be from 2 to 5 inclusive and we have
h(x) = f(x) - g(x), \(\displaystyle x\, \epsilon\, (-\infty,\, 2]\, or\, x\, \epsilon\, [2, 5]\)
pka
Elite Member
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- Jan 29, 2005
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The domain of \(\displaystyle \left( {\sqrt {5 - x} } \right) \cdot \left( {{x^2} - 4} \right)\)
will be \(\displaystyle \left( { - \infty ,5} \right] \cap \left\{ {x:\left| x \right| \ge 2} \right\}\).
Note that set does not contain \(\displaystyle (-2,2)\)
When you say "the first one", I'm assuming you mean part a. If that's not the case, please correct me. To solve that, think about the domains of the individual parts. Since both f(x) and g(x) are under a square root, what do you know about their domains? In other words, when evaluating f(x) + g(x), which inputs of x would result in you having to take the square root of a negative number? Now you say in your post that you tried the answer [2,5] and it was wrong. But do you know why that was wrong? With that answer, you're saying that the expression only works for x values between 2 and 5, inclusively.
As for how to format your answers using the union symbol and all that... I can't really help you. Online grading software is notorious for being demanding. It expects it written exactly one way and anything else is automatically wrong. Once you find the answers, I'd ask your instructor for advice on how to get the software to accept those answers.
As for how to format your answers using the union symbol and all that... I can't really help you. Online grading software is notorious for being demanding. It expects it written exactly one way and anything else is automatically wrong. Once you find the answers, I'd ask your instructor for advice on how to get the software to accept those answers.