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Consider the functionsf(x) = \sqrt{\dfrac{x+1}{x-1}}\qquad\qquad\text{and}\qquad\qquad g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}.Explain why f and g are not the same function.

 Nov 6, 2014
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For numbers smaller than -1, g(x) will have a negative number under the radical sign, will be undefinded for real numbers.

However, f(x), for values less than -1, both the numerator and the denominator will be negative, giving a positive answer, and will then be defined.

The functions will be equaivalent if x > -1; for x ≤ -1, f(x) will be defined but g(x) won't be.

 Nov 6, 2014

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