Posted by Jasmin on Saturday, June 13, 2009 at 1:41am.
Let (gx)= 10x/2+x
Please Help
(a) Find g (–1).
(b) State the domain of the function .
(c) Find g (t + 1) and simplify as much as possible.

Algebra  drwls, Saturday, June 13, 2009 at 6:26am
You need to add parentheses to define the numerator and denominator.
Do you mean g(x) = (10x)/(2+x), or
10  (x/2) + x ?
Other interpretations are also possible. They are not the same function 
Algebra  Jasmin, Saturday, June 13, 2009 at 9:03am
10x is on the top and 2+x is on the bottom then it asks for
(a) Find g (–1).
(b) State the domain of the function .
(c) Find g (t + 1) and simplify as much as possible.
Does this ans your ? I am really confused and need help. Thanks! 
Algebra  Reiny, Saturday, June 13, 2009 at 9:40am
I don't think drwls is still here, so I will reply instead.
so we have
(gx)= (10x)/(2+x)
then g(1) = (10(1))/(2+(1))
= 11/1 = 11
(notice is simply replaced the x with 1 wherever it showed up)
the domain is simply your choice of numbers for x which will result in a real number.
so in (10x)/(2+x) we can sub in any value of x except x=2 which would result in the denominator equal to zero.
Of course a division by zero is undefined, thus no real number answer.
for g(t+1) we replace any x we see with t+1
so g(t+1) = (10  (t+1))/(2+(t+1))
= (9t)/(3+t) 
Algebra  Jasmin, Saturday, June 13, 2009 at 9:43am
Why do we use t as a variable? What should I be looking for as I figure this out?

Algebra  Jasmin, Saturday, June 13, 2009 at 9:47am
Is t only used in part c?

Algebra  Reiny, Saturday, June 13, 2009 at 9:53am
your question was
<< (c) Find g (t + 1) and simplify as much as possible. >>
so I replaced x with tt+1 and simplified
e.g. g(☻) = (10☻)/(2+☻) 
Algebra  Jasmin, Saturday, June 13, 2009 at 10:03am
So the domain is any set of real numbers? What would the domain part look like?
for "a" g(1)= 11
and g (1) = (10(1))/ (2+ (1))
= 11/1 = 11 
Algebra  Reiny, Saturday, June 13, 2009 at 10:25am
it depends on your equation.
for a function of the form
f(x) = 'any algebraic expression containing some x's'
the "domain" is the set of all the x's you can choose from to obtain a real number as an answer.
the "range" is the set of all those real numbers you get, or all those f(x) results.
The most common problems with domain arise when ..
1. there is a denominator which turns to zero for some value or values of x
e.g. in yours there is a denominator of (2+x)
Doesn't 2+x become zero when x=2
That is why your domain is the set of all real numbers except x=2
2. if your equation contains a square root of some expression, which becomes negative for some value or values of x
Since we cannot take the square root of a negative number, all those guilty x's have to be exclude.
e.g. f(x) = √(x+5)
all x < 5 would cause a problem, so the domain is :set of all real numbers, except x < 5 
Algebra  Jasmin, Saturday, June 13, 2009 at 10:36am
So for mine the answer would be
(infinity,2) U (2,infinity)? 
Algebra  Reiny, Saturday, June 13, 2009 at 10:48am
not familiar with your notation for domain
in the good ol' days we would have written this domain as
domain = {x │ x (the 'is an element' symbol) R, x ≠ 2} 
Algebra  Jasmin, Saturday, June 13, 2009 at 10:56am
So is my answer correct?
(infinity,2) U (2,infinity)? 
Algebra  Reiny, Saturday, June 13, 2009 at 11:03am
Did you not read my reply??
your answer of (infinity,2) U (2,infinity) contains the UNION symbol
which means any element in the first set OR any element in the second set.
I would conclude you want 2 to be included.
But that would be wrong!
the 2 has to be excluded. 
Algebra  Jasmin, Saturday, June 13, 2009 at 11:18am
So what if i take the U symbol away and leave infinity, 2 and 2 infinity. would this be correct?