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March 28, 2017

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Find the domain, range, and inverse of the function f(x)=arcsin(sqrt(x))

  • Calculus - ,

    given:
    y = arcsin √x
    or
    √x = sin y

    domain: clearly 0 ≤ x ≤ 1
    and the domain is : y any real number

    for inverse:
    interchange the x and y in
    √x = sin y
    to get
    √y = sinx
    y = sin^2 x

    so f^-1 (x) = sin^2 x or (sinx)^2

    verification:
    http://www.wolframalpha.com/input/?i=plot+√x+%3D+sin%28y%29

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