Anonymous
Anonymous asked in Science & MathematicsMathematics · 7 years ago

From the formula, k(x)=2sin(x+pi)/(sin(x+pi)-3), what is k^-1(x)?

Also what is k^-1(k(x))=x?

1 Answer

Relevance
  • 7 years ago
    Favorite Answer

    k(x) = 2 sin (x+π) / (sin (x+π) - 3)

    = 2 (- sin x) / (- sin x - 3)

    = 2 sin x / (sin x + 3)

    = [2 (sin x + 3) - 6] / (sin x + 3)

    = 2 - 6 / (sin x + 3)

    So for k^-1(x) we get

    x = 2 - 6 / (sin k^-1(x) + 3)

    => 6 / (sin k^-1(x) + 3) = 2 - x

    => sin k^-1(x) + 3 = 6 / (2 - x)

    => sin k^-1(x) = 6 / (2 - x) - 3 = (6 - 6 + 3x) / (2 - x) = 3x / (2-x)

    => k^-1(x) = arcsin (3x / (2-x)).

Still have questions? Get your answers by asking now.