What is f(x)/f(x+1) equal to?

Correct Answer is : −f(x2)-f(x²)−f(x2)

Correct Answer is : −f(x2)-f(x²)−f(x2)

Test Index

UPSC NDA II 2025 Mathematics Paper

Question Numbers: 76-77

For the following two (02) items:

Consider the function

f(x)=\frac{x}{1-x}(x>0,x≠1)

Question : 76 of 120

Marks: +1, -0

What is

\frac{f(x)}{f(x+1)}

equal to?

Solution:

Concept:

Given

f(x)=\frac{x}{1-x}

, find

f(x+1)

and then compute the ratio

\frac{f(x)}{f(x+1)}

Explanation:

First,

f(x+1)=\frac{x+1}{1-(x+1)} = \frac{x+1}{-x}

Now, compute the ratio:

\frac{f(x)}{f(x+1)} = \frac{\frac{x}{1-x}}{\frac{x+1}{-x}} = \frac{x}{1-x} \cdot \frac{-x}{x+1} = \frac{-x^2}{(1-x)(x+1)} = \frac{-x^2}{1-x^2}

Notice that

-f(x^2) = -\frac{x^2}{1-x^2} = \frac{-x^2}{1-x^2}

Hence,

\frac{f(x)}{f(x+1)} = -f(x^2)

Answer:

-f(x^{2})

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