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1. relation and function — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths1. relation and function1 Mark
MCQ
Let the function $f$ be defined by $f(x) = \frac{{2x + 1}}{{1 - 3x}}$, then ${f^{ - 1}}(x)$ is
  • ✓
    $\frac{{x - 1}}{{3x + 2}}$
  • B
    $\frac{{3x + 2}}{{x - 1}}$
  • C
    $\frac{{x + 1}}{{3x - 2}}$
  • D
    $\frac{{2x + 1}}{{1 - 3x}}$
✓

Answer

Correct option: A.
$\frac{{x - 1}}{{3x + 2}}$
a
(a) Let $y = f(x)$ ==> $y = \frac{{2x + 1}}{{1 - 3x}}$

==> $y - 3xy = 2x + 1$

==> $x = \frac{{y - 1}}{{3y + 2}}$ 

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

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

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