Anonymous
Anonymous asked in Science & MathematicsMathematics · 9 years ago

Find the domain and range of following function?

3/√x-3

please explain

4 Answers

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  • 9 years ago
    Favorite Answer

    well domain is any acceptable x values. There can be no negatives under a radical and 0 cant be in the denominator so its x>3

    range is the possible y values and that is going to simply be y>0

    Source(s): Took AP calc in HS
  • Anonymous
    9 years ago

    The domain is x > 3, xEℝ.

    The smallest number that you can put into that function that doesn't result in having to square root a negative is 3. But then you would have to divide by 0 which is impossible, so the next biggest integer you can use is 4.

    In short, when you have to find the domain of a function, just find the smallest number you can put into that function without getting a maths error.

    ----

    To find the range, I put 3 into the function (3 / √(4-3) = 3√1 = 1). So the range is y ≥ 1 yEℝ. Since I can't use negative numbers that's the smallest value of y that I can get with that function.

    Hope this helps!

    Source(s): My maths teacher
  • QC
    Lv 7
    9 years ago

    Without parentheses, we get only √x in denominator:

    y = (3/√x) - 3

    So domain is all values of x that do not make denominator 0 (x ≠ 0)

    and all values of x that do not make value under √ negative (x ≥ 0)

    Combining these results, we get: x > 0

    Range:

    (3/√x) > 0

    (3/√x) - 3 > -3

    y > -3

    Domain: (0, ∞)

    Range: (-3, ∞)

    --------------------

    Perhaps you meant y = 3/(√x - 3)

    with only x under √

    Denominator cannot be 0 ----> √x ≠ 3 ----> x ≠ 9

    Value under √ cannot be negative -----> x ≥ 0

    Domain: [0, 9) U (9, ∞)

    When x is between 0 and 9, denominator < 0 and ≥ -3 ----> y ≤ -1

    When x is > 9, denominator > 0 -----> y > 0

    Range: (-∞, -1) U (0, ∞)

    --------------------

    Perhaps you meant y = 3/√(x - 3)

    with all of x-3 under √

    Denominator cannot be 0 ----> x - 3 ≠ 0 ----> x ≠ 3

    Value under √ cannot be negative -----> x - 3 ≥ 0 ----> x ≥ 3

    Combining these results, we get: x > 3

    Domain: (3, ∞)

    Since both numerator and denominator are both > 0, then y > 0

    Range: (0, ∞)

    --------------------

    Next time you may want to use parentheses to avoid confusion.

    Mαthmφm

  • 9 years ago

    Since denominator can't be neg solve √x-3 >/= to 0 . . .

    So the domain will be all reals >/= to 9.

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