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Factorisation by Common Factors

If fx = 3x2...

Question

If $f (x) = 3 x^{2} - 5 x - 4$ , then $f (- 2 x)$ is equal to

2 f (- x)

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- f (x)

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4 f (x)

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- 4 f (x)

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none of these

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Solution

The correct option is E none of these
Given, $f (x) = 3 x^{2} - 5 x - 4$ .......(1)
So $f (- 2 x) = 12 x^{2} + 10 x - 4$
$\Rightarrow 2 f (- x) = 6 x^{2} + 10 x - 8$ ...... from (1)
$\Rightarrow - f (x) = - 3 x^{2} + 5 x + 4$
$\Rightarrow 4 f (x) = 12 x^{2} - 20 x - 16$
$\Rightarrow - 4 f (x) = - 12 x^{2} + 20 x + 16$
Therefore, the correct answer is option $E$ .

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