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

In interval notation. Any help would be greatly appreciated!

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- FazLv 71 decade agoFavorite 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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