If 2 f(x)+f(1-x)=x, then what is f(x) equal to?

Correct Answer is : x−(13){x}-≤ft(1/3)x−(31)

Correct Answer is : x−(13){x}-≤ft(1/3)x−(31)

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UPSC NDA I 2026 Mathematics Paper

Question : 80 of 120

Marks: +1, -0

2 f(x)+f(1-x)=x

f(x)

equal to?

Solution:

Concept:

Replace

x

1-x

to get a second equation, then solve the two linear equations for

f(x)

Explanation:

Given:

2f(x)+f(1-x)=x

Replace

x

1-x

2f(1-x)+f(x)=1-x

Multiply the second equation by 2:

4f(1-x)+2f(x)=2-2x

Subtract the first equation:

3f(1-x)=2-3x

So:

f(1-x)=\frac{2-3x}{3}

Put

x \to 1-x

f(x)=\frac{2-3(1-x)}{3}=\frac{3x-1}{3}=x-\frac{1}{3}

Answer:

f(x)=x-\frac{1}{3}

, which is option B.

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