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Relations and Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsRelations and Functions1 Mark
MCQ
If $2\text{f(x)}-3\text{f}\Big(\frac{1}{\text{x}}\Big)=\text{x}^2(\text{x}\neq0),$ then $f(2)$ is equal to:
  • ✓
    $-\frac{7}{4}$
  • B
    $\frac{5}{2}$
  • C
    $-1$
  • D
    None of these.
✓

Answer

Correct option: A.
$-\frac{7}{4}$
$2\text{f(x)}-3\text{f}\Big(\frac{1}{\text{x}}\Big)=\text{x}^2\ ...(\text{i})$ $(\text{x}\neq0)$
Replacing $x$ by $\frac{1}{\text{x}}$
$2\text{f}\Big(\frac{1}{\text{x}}\Big)-3\text{f(x)}=\frac{1}{\text{x}^2}\ ...(\text{ii})$
Solving equations $(i)\ \&\ (ii)$
$-5\text{f(x)}=\frac{3}{\text{x}^2}+2\text{x}^2$
$\Rightarrow\text{f(x)}=\frac{-1}{5}\Big(\frac{3}{\text{x}^2}+2\text{x}^2\Big)$
Thus, $\text{f(2)}=\frac{-1}{5}\Big(\frac{3}{4}+2\times4\Big)$
$=\frac{-1}{5}\Big(\frac{3+32}{4}\Big)$
$=-\frac{7}{4}$

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