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

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$[- 34, 34]$

$[0, 34]$

$[- 34, 17]$

$[- 34, 0]$

answer is D.

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Detailed Solution

$ƒ (7) + ƒ (- 7) = - 10 ∴ ƒ (7) = - 17 ƒ (7) + 17 \cos x = - 17 + 17 \cos x$

Which has range $[- 34, 0]$

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