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1.Relation and Function
easy
Let the function $f$ be defined by $f(x) = \frac{{2x + 1}}{{1 - 3x}}$, then ${f^{ - 1}}(x)$ is
A
$\frac{{x - 1}}{{3x + 2}}$
B
$\frac{{3x + 2}}{{x - 1}}$
C
$\frac{{x + 1}}{{3x - 2}}$
D
$\frac{{2x + 1}}{{1 - 3x}}$
Solution
(a) Let $y = f(x)$ ==> $y = \frac{{2x + 1}}{{1 – 3x}}$
==> $y – 3xy = 2x + 1$
==> $x = \frac{{y – 1}}{{3y + 2}}$
==> ${f^{ – 1}}(y) = \frac{{y – 1}}{{3y + 2}}$
$\Rightarrow {f^{ – 1}}(x) = \frac{{x – 1}}{{3x + 2}}$.
Standard 12
Mathematics