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NDA 2026
Exam
NDA
Year
2026
Subject
Mathematics
Chapter
Functions

NDA 2026 · Mathematics · Functions

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

If 2f(x)+f(1−x)=x2f(x)+f(1-x)=x, then what is f(x)f(x) equal to ?

Options

  1. Ax−1x-1
  2. Bx−(13)x- \left(\dfrac{1}{3}\right)
  3. C2x2x
  4. D2x−12x-1

Correct answer

B. x−(13)x- \left(\dfrac{1}{3}\right)

Step-by-step solution

Given equation is 2f(x)+f(1−x)=x2f(x) + f(1-x) = x.

Replacing xx with 1−x1-x, we get:

2f(1−x)+f(x)=1−x2f(1-x) + f(x) = 1-x

Multiplying the first equation by 22, we get:

4f(x)+2f(1−x)=2x4f(x) + 2f(1-x) = 2x

Subtracting the second equation from this, we get:

3f(x)=2x−(1−x)3f(x) = 2x - (1-x)

3f(x)=3x−13f(x) = 3x - 1

f(x)=x−13f(x) = x - \dfrac{1}{3}

Answer: $x- \left(\dfrac{1}{3}\right)
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