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Posted by on Saturday, June 13, 2009 at 1:41am.

Let (gx)= 10-x/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 - , Saturday, June 13, 2009 at 6:26am

    You need to add parentheses to define the numerator and denominator.

    Do you mean g(x) = (10-x)/(2+x), or
    10 - (x/2) + x ?

    Other interpretations are also possible. They are not the same function

  • Algebra - , Saturday, June 13, 2009 at 9:03am

    10-x 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 - , Saturday, June 13, 2009 at 9:40am

    I don't think drwls is still here, so I will reply instead.

    so we have
    (gx)= (10-x)/(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 (10-x)/(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))
    = (9-t)/(3+t)

  • Algebra - , 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 - , Saturday, June 13, 2009 at 9:47am

    Is t only used in part c?

  • Algebra - , 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 - , 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 - , 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 - , Saturday, June 13, 2009 at 10:36am

    So for mine the answer would be

    (-infinity,-2) U (-2,infinity)?

  • Algebra - , 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 - , Saturday, June 13, 2009 at 10:56am

    So is my answer correct?

    (-infinity,-2) U (-2,infinity)?

  • Algebra - , 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 - , 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?

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