Relations and Functions — Class 12 Maths Solution

exemplar objective MCQ NCERT Exemp.Q.42,Page 15
Question

If $f:R - \left\{ {\frac{3}{5}} \right\} \to R$ be defined by $f(x) = \frac{{3x + 2}}{{5x - 3}}$, then

  • (a) ${f^{ - 1}}(x) = f(x)$ ✓ Correct
  • (b) ${f^{ - 1}}(x) = - f(x)$
  • (c) $(fof)x = - x$
  • (d) ${f^{ - 1}}(x) = \frac{1}{{19}}f(x)$
Step-by-step Solution
Correct answer: option (a)

It is given that,, $f(x) = \frac{{3x + 2}}{{5x - 3}}$
Let $y = \frac{{3x + 2}}{{5x - 3}}$

$3x + 2 = 5xy - 3y \Rightarrow x(3 - 5y) = - 3y - 2$

$x = \frac{{3y + 2}}{{5y - 3}} \Rightarrow {f^{ - 1}}(x) = \frac{{3x + 2}}{{5x - 3}}$

$\therefore {f^{ - 1}}(x) = f(x)$

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Relations and Functions. Curated by Sachin Sharma. Free for all students.