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March 26, 2017

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What is range of this rational function:

20/1+x^2

  • Math - ,

    I assume you mean
    f(x)=20/(1+x²)
    Parentheses are important when posting mathematical formulas because with multiplication/division taking precedence over addition and subtraction, the posted function would not be very meaningful.

    The domain of a function means the values that x can take up, which in this case, is ℝ (= all real numbers).
    The range of a function is the range of values f(x) can take up for any possible values of x.
    In this case, the maximum is when x=0, which gives f(0)=20.
    The minimum is lim x->∞ f(x)=0.
    Therefore the range of the given function is
    ]0,20], or altrenatively, (0,20] in interval notation.

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