anonymous
  • anonymous
"given f(x)=x^2 what is the domain of g(x)=f(x+2)-5"
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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rsadhvika
  • rsadhvika
Any kind of transformation on a parabola will not change its domain.
anonymous
  • anonymous
this is a composition isn't it?
rsadhvika
  • rsadhvika
Having said that, g(x) domain would be same as f(x)

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rsadhvika
  • rsadhvika
It is a composition, you can look at it as transformation also.
rsadhvika
  • rsadhvika
Oops ! I was wrong
rsadhvika
  • rsadhvika
We need to work this as composition only
anonymous
  • anonymous
so it wouldn't just be the domain of: g(f(x))=(x^2 +2)-5
anonymous
  • anonymous
is that the proper composition? and then you find the domain that way?
rsadhvika
  • rsadhvika
There is a trick, which simplifies finding the domain
rsadhvika
  • rsadhvika
g(x)=f(x+2)-5
rsadhvika
  • rsadhvika
what values we feeding in to g(x) ? Those all are output given by f only
anonymous
  • anonymous
so x is in the domain of real numbers with no restrictions? like x^2?
rsadhvika
  • rsadhvika
g(x) never gets a value less than 2 to its input.
rsadhvika
  • rsadhvika
Domain of g(x) : x > = 2
anonymous
  • anonymous
why???
anonymous
  • anonymous
um this is kind of confusing. would you mind just telling me if I composed the function properly?
anonymous
  • anonymous
g(f(x))=(x^2 +2)-5
rsadhvika
  • rsadhvika
hold on the composition for a bit. Domain of f(x) : all reals Range of f(x) : x > 0 Domain of g(x) is the Range of f(x)
rsadhvika
  • rsadhvika
On second thoughts, Domain of g(x) is : x >= 0, which is the range of f(x)
rsadhvika
  • rsadhvika
Still its confusing ?
cwrw238
  • cwrw238
g(x) = (x + 2)^2 - 5 = x^2 + 4x - 1 the domain of f(x) is all real x the domain of g(x) is the same as f(x)
rsadhvika
  • rsadhvika
thats wrong cwrw, we need to see f(x) and g(x) as composition. your working makes g(x) isolated
cwrw238
  • cwrw238
the range of g(x) is [-5, + infinity)
rsadhvika
  • rsadhvika
g(x) never gets a negative value at its input because, all values it gets in input are fed from the output of f
cwrw238
  • cwrw238
yes i see your point - but the question is somewhat ambiguous
cwrw238
  • cwrw238
i'm confused also lol
rsadhvika
  • rsadhvika
^agree it seems ambiguous first read
rsadhvika
  • rsadhvika
I twisted the answer so many times before seeing it a bit clearly.. seems Cutie ran away lol
cwrw238
  • cwrw238
yea
cwrw238
  • cwrw238
can g(x) be a composition? if so whats the function h in g(x) = h(f(x) ?
rsadhvika
  • rsadhvika
i would see it like this proly : h is a simply composition g is a mix of composition and transformation
rsadhvika
  • rsadhvika
*simple
anonymous
  • anonymous
sorry, i was really just confused about the wording too. does the way the f was placed mean the question is really what is the domain of g(fx) or something else?
rsadhvika
  • rsadhvika
we can see it like this :- let h(x) = x+2 g(x) = f(h(x)) - 5
rsadhvika
  • rsadhvika
we still need to find domain of g(x) only
rsadhvika
  • rsadhvika
if you think f(h(x)) as variable t g(x) = t-5
rsadhvika
  • rsadhvika
t can take only values : t >= 0
rsadhvika
  • rsadhvika
so domain is [0, +inf)
cwrw238
  • cwrw238
i've just input the problem into the wolfram alpha math software program. it ignored the f\9x) = x^2 bit and came back with the domain of g(x) being all real numbers i think theres something wrong with the question
rsadhvika
  • rsadhvika
interesting, can you give the link
John_ES
  • John_ES
The domain is all real numbers, g(x) is defined for all inputs x in R.
cwrw238
  • cwrw238
http://www.wolframalpha.com/input/?i=given+f%28x%29%3Dx%5E2+what+is+the+domain+of+g%28x%29%3Df%28x%2B2%29-5
rsadhvika
  • rsadhvika
question clearly says g is a composition of f
cwrw238
  • cwrw238
hhmmm - i dont think so
John_ES
  • John_ES
Even if it is a composition, the domain is still all R. However if g(x)=Log(x) it would be another story,
rsadhvika
  • rsadhvika
@cwrw238 see this http://www.wolframalpha.com/input/?i=given+f%28x%29%3Dlog%28x%29++what+is+the+range+of+g%28x%29%3Df%28x%2B2%29-5
rsadhvika
  • rsadhvika
would like to see wat @UnkleRhaukus thinks
dumbcow
  • dumbcow
by definition \[f(x+2) = (x+2)^{2}\] thus \[g(x) = (x+2)^{2} -5\] so domain of g is all real numbers @rsadhvika had it right at first then a lot of over analyzing i guess
anonymous
  • anonymous
f(x) is a polynomial function whose domain is all reals:|dw:1371239029954:dw|
anonymous
  • anonymous
g(x) is a function with the same shape but translated over by 2 and down by 5|dw:1371239086433:dw|
anonymous
  • anonymous
The domain shouldn't change though, surely!
cwrw238
  • cwrw238
right

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