What is \frac{f(x)}{f(x+1)} equal to?
For the following two (02) items: Consider the function f(x)=\frac{x}{1-x} (x \gt 0, x \neq 1).
- A. -f(x^2) ✓
- B. -f(\sqrt{x})
- C. f(x^2)
- D. f(x-1)
Correct Answer: A. -f(x^2)
Explanation
We have f(x) = \frac{x}{1-x} and f(x+1) = \frac{x+1}{1-(x+1)} = \frac{x+1}{-x}. Dividing them gives \frac{f(x)}{f(x+1)} = \frac{x}{1-x} \times \frac{-x}{x+1} = \frac{-x^2}{1-x^2}. Since f(x^2) = \frac{x^2}{1-x^2}, the result is -f(x^2).
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