IF fx-2x-3-x-2-x- 2 and x- R- then f6f12

The correct option is A 45/32 f(x)= 2x+3x 2 f(6)= 2×6+36 2 f(6)= 154 f(12)= 2×12+312 2 f(12)= 83 Now f(6)f(12)= 4532 ...

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Standard XII

Mathematics

Algebra of Derivatives

IF fx=2x+3/...

Question

IF $f (x) = \frac{2 x + 3}{x - 2}, x \neq 2$ and $x ϵ R$ , then $\frac{f (6)}{f (\frac{1}{2})}$

\frac{35}{45}

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\frac{- 35}{45}

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\frac{- 45}{32}

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\frac{45}{35}

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Solution

The correct option is A $\frac{- 45}{32}$
$f (x) = \frac{2 x + 3}{x - 2}$

$f (6) = \frac{2 \times 6 + 3}{6 - 2}$

$f (6) = \frac{15}{4}$

$f (\frac{1}{2}) = \frac{2 \times \frac{1}{2} + 3}{\frac{1}{2} - 2}$

$f (\frac{1}{2}) = \frac{- 8}{3}$

Now

$\frac{f (6)}{f (\frac{1}{2})} = \frac{- 45}{32}$

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IF f(x)=2x+3x−2,x≠2 and xϵR, then f(6)f(12)

The correct option is A −4532f(x)=2x+3x−2f(6)=2×6+36−2f(6)=154f(12)=2×12+312−2f(12)=−83Nowf(6)f(12)=−4532

IF $f (x) = \frac{2 x + 3}{x - 2}, x \neq 2$ and $x ϵ R$ , then $\frac{f (6)}{f (\frac{1}{2})}$

The correct option is A $\frac{- 45}{32}$
$f (x) = \frac{2 x + 3}{x - 2}$

$f (6) = \frac{2 \times 6 + 3}{6 - 2}$

$f (6) = \frac{15}{4}$

$f (\frac{1}{2}) = \frac{2 \times \frac{1}{2} + 3}{\frac{1}{2} - 2}$

$f (\frac{1}{2}) = \frac{- 8}{3}$

Now

$\frac{f (6)}{f (\frac{1}{2})} = \frac{- 45}{32}$