First slide

Functions (XII)

Question

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

Moderate

A

$[- 34, 0]$
B

$[0, 34]$
C

$[- 34, 34]$
D

None of these

Solution

$f (7) + f (- 7) = - 10$
$f (7) = - 17$
$or f (7) + 17 \cos x = - 17 + 17 \cos x$
which has the range [-34, 0].

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