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Simple question on polynomials

  1. Feb 5, 2007 #1
    If f(x)=x^2 - 4x, determine an expression for g(x)

    g(x) = f(x + 2)

    How would I substitute f(x) when they are separated?

    my attempt

    g(x) = x^2 - 4x (x + 2)
  2. jcsd
  3. Feb 5, 2007 #2
    OK, first are you happy with this one: we have f(x) = x^2 - 4x, what is f(a)?
    (Answer: f(a) = a^2 - 4a. i.e. you just plug a into wherever x used to appear. It does NOT mean "f(a) = f(x) * a", which is similar to what you seem to have done in your attempt.)

    Now, use the same technique for f(x+2). We just plug (x+2) into wherever x used to appear. What do you reckon the answer should be?

    Once you have written f(x+2) as a polynomial, then we can call it g(x), or h(x) or y(x). So the "g(x) = " bit isn't that important.
  4. Feb 5, 2007 #3
    Ok so the solution would be:

    (x + 2) ^2 - 4x
    x^2 + 4x - 4X + 4

    answer: x^2 + 4
  5. Feb 5, 2007 #4
    Almost. You skipped substituting (x+2) in for one of your x's.
  6. Feb 6, 2007 #5


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    It will be a lot easier if you use "a+2" instead of "x+2" then switch it back so you know you swapped them all. Much harder to make a mistake.
  7. Feb 6, 2007 #6
    f(x)=x^2 -4x

    f(2) = 2^2 -4*2
    f(3) = 3^2 -4*3
    f(m) = m^2 -4*m
    whatever is inside those parenthesis next to f, you're going to substitute for every x inside the original function.

    f( :approve: ) = :approve: ^2 -4*:approve:

    What helps sometimes is to just put in parenthesis where x is, then go back and fill them in...

    (____)^2 - 4*(____)

    Then, put into those parenthesis whatever is f(HERE)
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