Verified Solution • 2025–26 Session moderate

QJEEM25Ma6459: JEE Main 2025 Mathematics - Class 12 JEEM25Ma6459 Solution: Let be a function such that . If the , then is equal to

Let f:R−{0}→Rf: \mathbb{R}-\{0\} \rightarrow \mathbb{R} be a function such that f(x)−6f(1x)=353x−52f(x)-6 f\left(\frac{1}{x}\right)=\frac{35}{3 x}-\frac{5}{2} . If the lim⁡x→0(1αx+f(x))=β;α,β∈R\lim\limits _{x \rightarrow 0}\left(\frac{1}{\alpha x}+f(x)\right)=\beta ; \alpha, \beta \in \mathbb{R} , then α+2β\alpha+2 \beta is equal to

Multiple Choice Options

  • A 6
  • B 5
  • C 3
  • D 4

Step-by-Step Verified Solution

F(x)−6f(1/x)=353x−52..... (1)F(x)-6 f(1 / x)=\frac{35}{3 x}-\frac{5}{2}\quad\text{..... (1)}

 Replace x→1xF(1/x)−6(x)=35x3−52..... (2) Using (1) & (2) f(x)=−2x−13x+12B=limx→0(1αx+f(x))

=limx→0(1αx−2x−13x+12)α=3,B=1/2 So, α+2B=3+1=4

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