calculus

Let f(x)=(x-1)/(-x^2+2)
a. Is this point (-1,-2/3) on the graph of f?
b. State the domain of f and then solve f(x) 1/2?

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asked by Staffon
  1. f(x) =(1-x)/(x^2-2)
    if x = -1
    f(-1) = 2/(-1) = -2
    so no, (-1 ,-2) is on the graph

    bottom is zero if x = sqrt 2 or if x = -sqrt 2 so domain is all real x except those two points
    f(1/2) = (1/2)/(1/4 - 2)
    = (2/4)/(-7/4)
    = -2/7

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    posted by Damon
  2. Damon,
    For a. you just plug in -1.
    f(-1)=(-1-1)/((-1)^2+2)= -2/3 ?
    so yes,(-1,-2/3) on the graph.

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    posted by Staffon
  3. if x = -1
    - x^2
    is
    -(-1*-1)
    -(1)
    -1
    but
    (-x)^2
    (-1)^2
    is
    +1

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    posted by Damon

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