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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Functions

NDA 2024 · Mathematics · Functions

Let 3 f(x)+f((1)/(x))=(1)/(x)+1 What is f(x) equal to?

Let 3f(x)+f(1x)=1x+13 f(x)+f\left(\frac{1}{x}\right)=\frac{1}{x}+1 What is f(x)f(x) equal to?

Options

  1. A18x−x8+14\frac{1}{8 x}-\frac{x}{8}+\frac{1}{4}
  2. B38x−x8+34\frac{3}{8 x}-\frac{x}{8}+\frac{3}{4}
  3. C38x+x8+14\frac{3}{8 x}+\frac{x}{8}+\frac{1}{4}
  4. D38x−x8+14\frac{3}{8 x}-\frac{x}{8}+\frac{1}{4}

Correct answer

D. 38x−x8+14\frac{3}{8 x}-\frac{x}{8}+\frac{1}{4}

Step-by-step solution

Given: 3f(x)+f\quad 3 f(x)+f\left(\frac{1}{x}\right)=\frac{1}{x}+1\quad ....(i)Replacing(Replacing (x)by(1x)) by \left(\frac{1}{x}\right), we get 3f(1x)+3 f\left(\frac{1}{x}\right)+ f(x)=x+1\quad ....(ii)Now,(i)×3−(ii)Now, (i) \times₃⁻(i i), we get 8f(x)=3x+3−x−1⇒f(x)=38x−x8+14....(8 f(x)=\frac{3}{x}+3-x-1\Rightarrow \quad f(x)=\frac{3}{8 x}-\frac{x}{8}+\frac{1}{4}\quad ....( iii)
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