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F(x) problem?

  1. Dec 24, 2004 #1
    if f(x)=x^2 write the equation for the transformed function y=2f(-1/2(x+5))-3

    the answer was y=1/2(x+5)^(2)-3

    How do u get this answer? What happened to the 2f? and the - in 1/2?

    Also how would the new function be graphed? What would it look like?
  2. jcsd
  3. Dec 24, 2004 #2


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    Here, 2f(-1/2(x+5))-3 does not mean 2 times f time -1/2(x+5) minus 3. It means, y is 2 times the function f(x)=x^2 where x is being replaced by the expression -1/2(x+5), minus 3.
  4. Dec 24, 2004 #3

    Doc Al

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    A less confusing way of writing it would be: f(g) = g^2. Now y = 2f(g) - 3, where g = -1/2(x+5). So: y = 2f(g) - 3 = 2g^2 - 3. You finish it by substituting for g.
  5. Dec 24, 2004 #4
    I hate Math text books that set the students up with badly written problem sets just to make them harder than they really are.

    though in all fairness, this could have been a starred question in the problem set.
  6. Dec 25, 2004 #5

    James R

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    The thing to realise about functional notation like f(x) is that x is a place holder. In other words, all of the following are equivalent definitions of the function f:

    f(x) = x^2
    f(y) = y^2
    f(stuff) = (stuff)^2
    f(_) = _^2

    In your expression for y, we see f(-1/2(x+5))

    Since f(anything) = anything^2, we get:

    f(-1/2(x+5)) = (-1/2(x+5))^2 = 1/4(x+5)^2

    Now y is another function, defined to be:

    y(x) = 2x - 3


    y(_) = 2 × _ - 3

    We want y(f(-1/2(x+5))). Putting it all together:

    y(f(-1/2(x+5))) = y(1/4(x+5)^2) = 2 [1/4(x+5)^2] - 3 = 1/2(x+5)^2 - 3
  7. Dec 25, 2004 #6
    Thanks everyone esp James I totally get it now, but it is sort of complicated at first.
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