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Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

what is the domain?

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2 Answers

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  • 2 months ago
    Favorite Answer

    I see an unbalanced parenthesis after the "c" but I'm going to ignore it and suppose that the argument of the arcsin is (x/a + b).  So the quantity (x/a + b) must be between -1 and +1, inclusive.

    When x/a + b = -1, you have x/a = -b - 1, and x = -ab - a.

    When x/a + b = +1, you have x/a = 1 - b, and x = a - ab.

    The third choice in the list seems to be correct.

  • Pope
    Lv 7
    2 months ago

    You mean this?

    f(x) = sin⁻¹(x/a + b) + c

    a, b, c ∈ (-∞, 0)

    The domain of the sin⁻¹ function is [-1, 1], and the added constant is of no consequence.

    -1 ≤ x/a + b ≤ 1

    -1 - b ≤ x/a ≤ 1 - b

    -a - ab ≥ x ≥ a - ab ... (multiplication by a, a negative)

    a - ab ≤ x ≤ -a - ab

    a(1 - b) ≤ x ≤ -a(1 + b)

    Domain: [a(1 - b), -a(1 + b)]

    That is the second choice on the list.

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