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

MCQ

Let the function $f$ be defined by $f(x)=\frac{2 x+1}{1-3 x}$ then $f^{-1}(x)$ is:

✓
$\frac{x-1}{3 x+2}$
B
$\frac{x+1}{3 x-2}$
C
$\frac{2 x+1}{1-3 x}$
D
$\frac{3 x+2}{x-1}$

✓

Answer

Correct option: A.

$\frac{x-1}{3 x+2}$

(A)
$\frac{x-1}{3 x+2}$
Hint:
$f(x)=\frac{2 x+1}{1-3 x}=y$, say. then
$2 \mathrm{x}+1=\mathrm{y}(1-3 \mathrm{x})$
$\therefore \mathrm{y}-1=\mathrm{x}(2+3 \mathrm{y}) $
$\therefore \mathrm{x}=\frac{y-1}{2+3 y}=\mathrm{f}^{-1}(\mathrm{y})$
$\therefore \mathrm{f}^{-1}(\mathrm{x})=\frac{x-1}{2+3 x}$

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