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

  • Calculus -

    y = arcsin √x
    √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


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