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Relations and Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsRelations and Functions1 Mark
MCQ
If $3\text{f(x)}+5\text{f}\Big(\frac{1}{\text{x}}\Big)=\frac{1}{\text{x}}-3$ for all non$-$zero $x,$ then $f(x) =$
  • A
    $\frac{1}{14}\Big(\frac{3}{\text{x}}+5\text{x}-6\Big)$
  • B
    $\frac{1}{14}\Big(-\frac{3}{\text{x}}+5\text{x}-6\Big)$
  • C
    $\frac{1}{14}\Big(-\frac{3}{\text{x}}+5\text{x}+6\Big)$
  • ✓
    None os these.
✓

Answer

Correct option: D.
None os these.
$3\text{f(x)}+5\text{f}\Big(\frac{1}{\text{x}}\Big)=\frac{1}{\text{x}}-3\ ...(\text{i})$
Multiplying $(1)$ by $3,$
$15\text{f}\Big(\frac{1}{\text{x}}\Big)+9\text{f(x)}=\frac{3}{\text{x}}-9\ ...(\text{ii})$
Replacing $x$ by $\frac{1}{\text{x}}$ in $(i)$
$3\text{f}\Big(\frac{1}{\text{x}}\Big)+5\text{f(x)}=\text{x}-3$
Multiplying by $5$
$15\text{f}\Big(\frac{1}{\text{x}}\Big)+25\text{f(x)}=5\text{x}-15\ ...(\text{iii})$
Solving $(ii)$ and $(iii),$
$-16\text{f(x)}=\frac{3}{\text{x}}-5\text{x}+6$
$\Rightarrow\text{f(x)}=\frac{1}{16}\Big(-\frac{3}{\text{x}}+5\text{x}-6\Big)$
Disclaimer: The question in the book has some error,
so, none of the options are matching with the solution.
The solution is created according to the question given in the book.

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