Q230 / 270 · NDA 2026 (Phase 1) · Mathematics
If $2f(x)+f(1-x)=x$, then what is $f(x)$ equal to ?
- A$x-1$
- Correct answerB$x-\left(\dfrac{1}{3}\right)$
- C$2x$
- D$2x-1$
Solution
Given equation is $2f(x) + f(1-x) = x$.
Replacing $x$ with $1-x$, we get:
$2f(1-x) + f(x) = 1-x$
Multiplying the first equation by $2$, we get:
$4f(x) + 2f(1-x) = 2x$
Subtracting the second equation from this, we get:
$3f(x) = 2x - (1-x)$
$3f(x) = 3x - 1$
$f(x) = x - \dfrac{1}{3}$
Answer: $x-\left(\dfrac{1}{3}\right)$
Replacing $x$ with $1-x$, we get:
$2f(1-x) + f(x) = 1-x$
Multiplying the first equation by $2$, we get:
$4f(x) + 2f(1-x) = 2x$
Subtracting the second equation from this, we get:
$3f(x) = 2x - (1-x)$
$3f(x) = 3x - 1$
$f(x) = x - \dfrac{1}{3}$
Answer: $x-\left(\dfrac{1}{3}\right)$
Hence, the correct answer is option: 'B'.