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1-40.

State the domain for each of the functions below. Homework Help ✎

  1. f(x) =

    We all know that 0 is excluded from the denominator of a fraction. What value of x, if any, would make the denominator x2 + 1 = 0?

  2. g(x) =

    Consider the domain of each part of the subtraction problem separately.

  3. h(x) =

    Typically, a square root function has a domain of x ≥ 0, but in this case, x is squared... meaning both positive or negative values will yield positive outputs. However, do not neglect to consider the − 9.
    What values of x, both positive and negative, will make x2 − 9 > 0?

    x ≤ − 3 U x ≥ 3

  4. k(x) =

    Consider the domain of the numerator and the domain of the denominator separately.

    I. What is the domain of log(x − 3)?

    III. What value is excluded from the denominator of all fractions?

    IV. Now combine these results to find the domain of k(x).

    I. x > 3
    II. x ≥ −4
    III. x ≠ −4
    IV. x > 3