Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

What is the range of sqrt(7+x)/sqrt(7-x)?

In interval notation. Any help would be greatly appreciated!

1 Answer

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  • Faz
    Lv 7
    1 decade ago
    Favorite Answer

    Multiply top and bottom by √(7-x) to get

    = √(7-x)√(7+x) / (7-x)

    = √(49-x²) / (7-x)

    = √(49(1 - x²/49 )) / (7-x)

    = 7√(1 - x²/49) / (7-x)

    Remember we can't take square roots of negative numbers.

    Solving (1 - x²/49) >= 0 gives -7<= x <= 7

    Domain is all x, x≠7, -7<= x < 7

    x=7 is a vertical asymptote

    Within the interval -7<= x < 7, the function is increasing (you can verify by finding the derivative) and continuous.

    Range is 0 =< f(x) < ∞, i.e. [0, ∞)

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