Let the function f be defined by f(x) = 2x + 1 1 - 3x , then f^ -… - Vidyadip

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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