The range of fx-2 x-2-3 x is

The correct option is B R {2/3} f(x) = y = 2x/2+3x ⇒ 2y+3yx = 2x ⇒ 2y = x (2 3y) ⇒ x = 2y/2 3y x is not defined when y= 2/3 Hence, the range of f(x) is R { ...

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Standard XI

Mathematics

Range

The range of ...

Question

The range of $f (x) = \frac{2 x}{2 + 3 x}$ is

$R$

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$R - {\frac{2}{3}}$

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$R - {\frac{- 2}{3}}$

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$R^{+}$

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Solution

The correct option is B
$R - {\frac{2}{3}}$

$f (x) = y = \frac{2 x}{2 + 3 x} \Rightarrow 2 y + 3 y x = 2 x \Rightarrow 2 y = x (2 - 3 y) \Rightarrow x = \frac{2 y}{2 - 3 y}$
$x$ is not defined when $y = \frac{2}{3}$
Hence, the range of f(x) is $R - {\frac{2}{3}}$

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The range of f(x)=2x2+3x is

The correct option is B R−{23} f(x)=y=2x2+3x⇒2y+3yx=2x⇒2y=x(2−3y)⇒x=2y2−3y x is not defined when y=23 Hence, the range of f(x) is R−{23}

The range of $f (x) = \frac{2 x}{2 + 3 x}$ is

The correct option is B
$R - {\frac{2}{3}}$

$f (x) = y = \frac{2 x}{2 + 3 x} \Rightarrow 2 y + 3 y x = 2 x \Rightarrow 2 y = x (2 - 3 y) \Rightarrow x = \frac{2 y}{2 - 3 y}$
$x$ is not defined when $y = \frac{2}{3}$
Hence, the range of f(x) is $R - {\frac{2}{3}}$