Let f - A - B be a function defined as f x - x -1- x -2- where A - R -2 and B - R -1 - Then f is -A- not invertibleB- invertible and f -1 y -3 y -1- y -1C- invertible and f -1 y -2 y -1- y -1D- invertible and f -1 y -2 y -1- y -1

The correct option is C invertible and f^ 1(y)=2y 1y 1Let f(x)=y=x 1x 2 ⇒ xy 2y=x 1 ⇒ x=2y 1y 1 As, f: R {2}→ R {1} satisfying So, f^ 1(y)=2y 1y 1 ...

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Byju's Answer

Standard XII

Mathematics

Properties of Inverse Function

Let f : A → B...

Question

Let $f : A \to B$ be a function defined as $f (x) = \frac{x - 1}{x - 2}$ , where $A = R - {2}$ and $B = R - {1}$ . Then $f$ is :

not invertible

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invertible and

f^{- 1} (y) = \frac{3 y - 1}{y - 1}

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invertible and

f^{- 1} (y) = \frac{2 y - 1}{y - 1}

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invertible and

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

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Solution

The correct option is C invertible and $f^{- 1} (y) = \frac{2 y - 1}{y - 1}$
Let $f (x) = y = \frac{x - 1}{x - 2}$
$\Rightarrow x y - 2 y = x - 1$
$\Rightarrow x = \frac{2 y - 1}{y - 1}$
As, $f : R - {2} \to R - {1}$ satisfying
So, $f^{- 1} (y) = \frac{2 y - 1}{y - 1}$

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Let f:A→B be a function defined as f(x)=x−1x−2, where A=R−{2} and B=R−{1}. Then f is :

The correct option is C invertible and f−1(y)=2y−1y−1Let f(x)=y=x−1x−2 ⇒xy−2y=x−1 ⇒x=2y−1y−1 As, f:R−{2}→R−{1} satisfying So, f−1(y)=2y−1y−1

Let $f : A \to B$ be a function defined as $f (x) = \frac{x - 1}{x - 2}$ , where $A = R - {2}$ and $B = R - {1}$ . Then $f$ is :

The correct option is C invertible and $f^{- 1} (y) = \frac{2 y - 1}{y - 1}$
Let $f (x) = y = \frac{x - 1}{x - 2}$
$\Rightarrow x y - 2 y = x - 1$
$\Rightarrow x = \frac{2 y - 1}{y - 1}$
As, $f : R - {2} \to R - {1}$ satisfying
So, $f^{- 1} (y) = \frac{2 y - 1}{y - 1}$