The range of f x - x -2- x -3 isA- R -3- -3 -2- - 0- -D- R -1

The correct option is D ℝ {1}f is defined for all x except where x 3=0 i.e., x=3 ∴ D(f)=ℝ {3} nbsp; Let y = x+2x 3 ⇒ xy 3y = x+2 ⇒ xy x =3y+2 ⇒ x = 3y+2y 1 ...

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Standard XI

Mathematics

Range

The range of ...

Question

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

R - {3}

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R - {1}

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(- \infty, - 3) \cup (- 2, \infty)

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(0, \infty)

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Solution

The correct option is B $R - {1}$
$f$ is defined for all $x$ except where $x - 3 = 0$ i.e., $x = 3$
$∴ D (f) = R - {3}$

Let $y = \frac{x + 2}{x - 3}$
$\Rightarrow x y - 3 y = x + 2$
$\Rightarrow x y - x = 3 y + 2$
$\Rightarrow x = \frac{3 y + 2}{y - 1}$
$x$ is defined for all $y \in R - {1}$
$∴ R (f) = R - {1}$

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Range

Standard XI Mathematics

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The range of f(x)=x+2x−3 is

The correct option is B R−{1}f is defined for all x except where x−3=0 i.e., x=3 ∴D(f)=R−{3} Let y=x+2x−3 ⇒xy−3y=x+2 ⇒xy−x=3y+2 ⇒x=3y+2y−1 x is defined for all y∈R−{1} ∴R(f)=R−{1}

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