Math

Let f(x) = (x - 1)/(-x2 + 2)
How to find the domain (Steps please)

Than solve for f(x)= 1/2

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asked by MSM
  1. F(x) = (x-1)/(-x^2+2).

    Any value of x that causes the denominator to become zero is not in the domain. Because a zero denominator
    means an undefined fraction.

    Denominator = -x^2 + 2 = 2- x^2.
    Set the denominator equal to zero and
    solve for x:

    2 - x^2 = 0,
    -x^2 = -2,
    x^2 = 2,
    x = +-sqrt(2) results in a denominator
    of zero, and is,therefore, NOT in the
    domain.

    So the domain is all real values of x
    except +- sqrt(2).

    F(1/2) = (1/2-1) / (2-(1/2)^2,
    F(1/2) = (-1/2) / (2-1/4),
    F(1/2) = (-1/2) / (7/4),
    F(1/2) = (-1/2) * 4/7 = -4/14 = -2/7.

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    posted by Henry

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