"given f(x)=x^2 what is the domain of g(x)=f(x+2)-5"

- anonymous

"given f(x)=x^2 what is the domain of g(x)=f(x+2)-5"

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- rsadhvika

Any kind of transformation on a parabola will not change its domain.

- anonymous

this is a composition isn't it?

- rsadhvika

Having said that, g(x) domain would be same as f(x)

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## More answers

- rsadhvika

It is a composition, you can look at it as transformation also.

- rsadhvika

Oops ! I was wrong

- rsadhvika

We need to work this as composition only

- anonymous

so it wouldn't just be the domain of: g(f(x))=(x^2 +2)-5

- anonymous

is that the proper composition? and then you find the domain that way?

- rsadhvika

There is a trick, which simplifies finding the domain

- rsadhvika

g(x)=f(x+2)-5

- rsadhvika

what values we feeding in to g(x) ? Those all are output given by f only

- anonymous

so x is in the domain of real numbers with no restrictions? like x^2?

- rsadhvika

g(x) never gets a value less than 2 to its input.

- rsadhvika

Domain of g(x) : x > = 2

- anonymous

why???

- anonymous

um this is kind of confusing. would you mind just telling me if I composed the function properly?

- anonymous

g(f(x))=(x^2 +2)-5

- 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

On second thoughts, Domain of g(x) is : x >= 0, which is the range of f(x)

- rsadhvika

Still its confusing ?

- 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

thats wrong cwrw, we need to see f(x) and g(x) as composition. your working makes g(x) isolated

- cwrw238

the range of g(x) is [-5, + infinity)

- 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

yes i see your point - but the question is somewhat ambiguous

- cwrw238

i'm confused also lol

- rsadhvika

^agree it seems ambiguous first read

- rsadhvika

I twisted the answer so many times before seeing it a bit clearly.. seems Cutie ran away lol

- cwrw238

yea

- cwrw238

can g(x) be a composition?
if so whats the function h in g(x) = h(f(x) ?

- rsadhvika

i would see it like this proly :
h is a simply composition
g is a mix of composition and transformation

- rsadhvika

*simple

- 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

we can see it like this :-
let h(x) = x+2
g(x) = f(h(x)) - 5

- rsadhvika

we still need to find domain of g(x) only

- rsadhvika

if you think f(h(x)) as variable t
g(x) = t-5

- rsadhvika

t can take only values : t >= 0

- rsadhvika

so domain is [0, +inf)

- 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

interesting, can you give the link

- John_ES

The domain is all real numbers, g(x) is defined for all inputs x in R.

- 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

question clearly says g is a composition of f

- cwrw238

hhmmm - i dont think so

- 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

@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

would like to see wat @UnkleRhaukus thinks

- 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

f(x) is a polynomial function whose domain is all reals:|dw:1371239029954:dw|

- anonymous

g(x) is a function with the same shape but translated over by 2 and down by 5|dw:1371239086433:dw|

- anonymous

The domain shouldn't change though, surely!

- cwrw238

right

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