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warpedkitten
 one year ago
If f(x) = x^2  25 and g(x) = x  5, what is the domain of (f/g)(x)?
warpedkitten
 one year ago
If f(x) = x^2  25 and g(x) = x  5, what is the domain of (f/g)(x)?

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UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2\[f(x) = x^225\] and \[g(x) = x5 \] \[(\frac{f}{g})(x)\] is this your question and are those the right functions?

warpedkitten
 one year ago
Best ResponseYou've already chosen the best response.0Yes, that's correct.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2alright so we need \[(\frac{f}{g})(x) \] \[(\frac{f}{g})(x) = \frac{x^225}{x5}\] can you factor the \[x^225\]? after that step we can cancel a term out

warpedkitten
 one year ago
Best ResponseYou've already chosen the best response.0I don't know how to solve it, I'm not very good with math. lol.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2oh ok. no problem . we can use the difference of squares formula \[(a^2b^2) = (a+b)(ab) \] so if we let a = x and b = 5 \[(x^25^2) = (x+5)(x5) \]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2so \[(\frac{f}{g})(x) = \frac{(x+5)(x5)}{x5}\] so what does the numerator and denominator have in common

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2there's a x5 in the numerator and denominator so that term is canceled out

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2\[(\frac{f}{g})(x) = x+5\] since our new function isn't a fraction , there are no restrictions so the domain is all real numbers.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2the graph should be a straight line and it's a function because it passes the vertical line test. A vertical line test is needed to determine if a graph is a function or not. If it's a function then the vertical line should hit the graph only once. If it's not a function, the vertical line crosses the graph more than once.

warpedkitten
 one year ago
Best ResponseYou've already chosen the best response.0So my answer options are all real values of x all real values of x except x = 5 all real values of x except x = –5 all real values of x except x = 5 and x = –5 Would that mean it's a? Since they're all real numbers? Or would it be b?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2has to be a... all reals. the function is not a fraction

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2this is the graph of the function (f/g) (x)

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2if you draw a vertical line on this graph, the vertical line only touches once, so it's a function .

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.0hehe domain does not include x=5. It would not show up on a graph because its a hole. If you graph \(\frac{x^225}{(x5)}\) and zoomed in infinitely close it would look like this dw:1439266602373:dw \[\frac{x^225}{(x5)}\ne x+5\] in general (one is defined for 5, one is not) But if we remove \(5\) from the domain it is :)

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2if we factor the numerator, the x5 cancels out leaving us with the new function no longer being a fraction. Hence, no restrictions... all reals. \[(\frac{f}{g})(x) = \frac{x^225}{x5} \] \[(\frac{f}{g})(x) = \frac{(x+5)(x5)}{x5}\] \[(\frac{f}{g})(x) = x+5 \]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2if you're not factoring then there is a restriction which is all reals except when x = 5. But I think that there have been times when canceling terms can happen.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2both \[(\frac{f}{g})(x) = \frac{(x+5)(x5)}{x5} \] and \[(\frac{f}{g})(x) = x+5 \] produce different results.. It's like do we consider the factored version in that case it's all reals on the domain or the nonfactored case all reals except x = 5 ?
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