math

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find the domain and range of:
the square root of 25-x^2

  • math -

    f(x)=√(25-x²)
    For f(x) to be real, we require that the expression 25-x² be non-negative, i.e.
    25-x²≥0 ....(1)
    (1) is satisfied when
    |x|≤5,
    or x∈[-5,5] which is exactly the domain of f(x).
    The range of f(x) varies from 0 when x=±5 to 5 when x=0.

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