F-5-4 given byfx-4x5-x- then

It can be inferred from the options nbsp; that f is bijective function. Let y=4x5 x ⇒ 5y xy=4x ⇒ 5y=xy+4x ⇒ 5y=x(y+4) ⇒ x=5yy+4 Replace x and y ⇒ y=5xx+4 ∴ f^ ...

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Standard XII

Mathematics

Convexity

f:ℝ-5→ℝ--4 gi...

Question

$f : R - {5} \to R - {- 4}$ given by $f (x) = \frac{4 x}{5 - x}$ , then

f^{- 1} (x) = \frac{5 x}{x - 4}

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f^{- 1} (x) = \frac{4 x}{x - 5}

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f^{- 1} (x) = \frac{4 x}{x + 5}

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f^{- 1} (x) = \frac{5 x}{x + 4}

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Solution

The correct option is D $f^{- 1} (x) = \frac{5 x}{x + 4}$
It can be inferred from the options that $f$ is bijective function.
Let $y = \frac{4 x}{5 - x}$
$\Rightarrow 5 y - x y = 4 x$
$\Rightarrow 5 y = x y + 4 x$
$\Rightarrow 5 y = x (y + 4)$
$\Rightarrow x = \frac{5 y}{y + 4}$
Replace $x$ and $y$
$\Rightarrow y = \frac{5 x}{x + 4}$
$∴ f^{- 1} (x) = \frac{5 x}{x + 4}$

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Convexity

Standard XII Mathematics

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f:R−{5}→R−{−4} given byf(x)=4x5−x, then

The correct option is D f−1(x)=5xx+4It can be inferred from the options that f is bijective function. Let y=4x5−x ⇒5y−xy=4x ⇒5y=xy+4x ⇒5y=x(y+4) ⇒x=5yy+4 Replace x and y ⇒y=5xx+4 ∴f−1(x)=5xx+4

$f : R - {5} \to R - {- 4}$ given by $f (x) = \frac{4 x}{5 - x}$ , then