Let f-43- be a function defined as fx - 4x3x-4 The inverse of f is map g- Range f - -43 given by

F(x) = nbsp;4x3x+4 nbsp; ( x ≠ 43 nbsp; ) Let f(x) =y nbsp; nbsp;⇒ y=4x3x+4 nbsp; nbsp; nbsp; nbsp;⇒ y(3x+4) =4x nbsp; nbsp; nbsp; ...

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Byju's Answer

Standard XII

Mathematics

Properties of Determinants

Let f:ℝ--43→ℝ...

Question

Let $f : R - {\frac{- 4}{3}} \to R$ be a function defined as $f (x) = \frac{4 x}{3 x + 4}$ The inverse of $f$ is map $g :$ Range $f \to R - {\frac{- 4}{3}}$ given by

g (y) = \frac{4 y}{3 - 4 y}

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g (y) = \frac{4 y}{4 - 3 y}

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g (y) = \frac{3 y}{3 - 4 y}

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g (y) = \frac{3 y}{4 - 3 y}

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Solution

The correct option is B $g (y) = \frac{4 y}{4 - 3 y}$
$f (x) = \frac{4 x}{3 x + 4} (x \neq - \frac{4}{3})$

Let $f (x) = y$

$\Rightarrow y = \frac{4 x}{3 x + 4}$

$\Rightarrow y (3 x + 4) = 4 x$
$\Rightarrow 3 x y + 4 y = 4 x$
$\Rightarrow 3 x y - 4 y = - 4 y$
$\Rightarrow x (3 y - 4) = - 4 y$

$\Rightarrow x = \frac{- 4 y}{3 y - 4} (y \neq \frac{4}{3})$

$\Rightarrow x = \frac{- 4 y}{- 1 (- 3 y + 4)}$

$\Rightarrow x = \frac{4 y}{(4 - 3 y)}$

So, inverse of $f$ is,

$f^{- 1} = \frac{4 y}{(4 - 3 y)}$

$∴ g (y) = \frac{4 y}{(4 - 3 y)}$

Hence, $B$ is the correct answer

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Similar questions

Letbe a function defined as. The inverse of f is map g: Range

(A) (B)

Q. Let

f : R - {- \frac{4}{3}} \to R

be a function defined as

f (x) = \frac{4 x}{3 x + 4}

. The inverse of

f

is the map

g : R a n g e f \to R - {- \frac{4}{3}}

given by

Let $f : R - {- \frac{4}{3}} \to R$ be a function defined as $f (x) = \frac{4 x}{3 x + 4}, x \neq - \frac{4}{3}$ . The inverse of f is the map g: Range $f \to R - {- \frac{4}{3}}$ is given by
$(a) g (y) = \frac{3 y}{3 - 4 y} (b) g (y) = \frac{4 y}{4 - 3 y} (c) g (y) = \frac{4 y}{3 - 4 y} (d) g (y) = \frac{3 y}{4 - 3 y}$