If fx=ax7+bx3+cx−5 where a,b,c∈R and f−7=7 then the range of f7+17cosx is

fx+f−x=−10 and sub x=7 ⇒ f7=−17, cosx∈[−1, 1]∴ f7+17 cosx=−17−17, −17+17=−34, 0

If fx=ax7+bx3+cx−5 where a,b,c∈R and f−7=7 then the range of f7+17cosx is

fx+f−x=−10 and sub x=7 ⇒ f7=−17, cosx∈[−1, 1]∴ f7+17 cosx=−17−17, −17+17=−34, 0

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If $f (x) = a x^{7} + b x^{3} + c x - 5$ where $a, b, c \in R$ and $f (- 7) = 7$ then the range of $f (7) + 17 \cos x$ is

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[-1, 1]

[-34, 0]

[-34, 34]

[0, 34]

answer is B.

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Detailed Solution

$f (x) + f (- x) = - 10$ and sub $x = 7 \Rightarrow f (7) = - 17, \cos x \in [- 1, 1]$

$∴ f (7) + 17 \cos x = [- 17 - 17, - 17 + 17] = [- 34, 0]$

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If fx=ax7+bx3+cx−5 where a,b,c∈R and f−7=7 then the range of f7+17cosx is

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If $f (x) = a x^{7} + b x^{3} + c x - 5$ where $a, b, c \in R$ and $f (- 7) = 7$ then the range of $f (7) + 17 \cos x$ is