If fx-2 x-5-x-3- then

The correct options are B Domain of f(x) is nbsp;ℝ { 3} nbsp; C Range of f(x) is nbsp;ℝ {2}f(x)=2x 5x+3 Since, f(x) is not defined at x= 3. Therefore, dom ...

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Standard XI

Mathematics

Method of Intervals

If fx=2 x-5/x...

Question

If $f (x) = \frac{2 x - 5}{x + 3},$ then

Domain of

f (x)

R

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Domain of

f (x)

R - {- 3}

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Range of

f (x)

R - {2}

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Range of

f (x)

R

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Solution

The correct options are
B Domain of $f (x)$ is $R - {- 3}$
C Range of $f (x)$ is $R - {2}$
$f (x) = \frac{2 x - 5}{x + 3}$
Since, $f (x)$ is not defined at $x = - 3.$
Therefore, domain $= R - {- 3}$
Let $y = \frac{2 x - 5}{x + 3}$
$\Rightarrow 2 x - 5 = x y + 3 y$
$\Rightarrow x (2 - y) = 3 y + 5$
$\Rightarrow x = \frac{3 y + 5}{2 - y}$
Clearly, $y \neq 2$
Therefore, range $= R - {2}$

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If f(x)=2x−5x+3, then

The correct options are B Domain of f(x) is R−{−3} C Range of f(x) is R−{2}f(x)=2x−5x+3 Since, f(x) is not defined at x=−3. Therefore, domain =R−{−3} Let y=2x−5x+3 ⇒2x−5=xy+3y ⇒x(2−y)=3y+5 ⇒x=3y+52−y Clearly, y≠2 Therefore, range =R−{2}

If $f (x) = \frac{2 x - 5}{x + 3},$ then