Question #b434a

Dec 10, 2016

$f \left(9\right) = - 15$

Explanation:

$f \left(x\right) = a {x}^{7} + b {x}^{5} + c {x}^{3} - 6$

$f \left(x\right) = g \left(x\right) - 6$

where

$g \left(x\right) = a {x}^{7} + b {x}^{5} + c {x}^{3}$

is an odd function such that $g \left(x\right) = - g \left(- x\right)$

Now if $f \left(- 9\right) = g \left(- 9\right) - 6 = 3$ then

$f \left(9\right) = g \left(9\right) - 6 = - g \left(- 9\right) - 6$ but

$g \left(- 9\right) = 9$ then

$f \left(9\right) = - 9 - 6 = - 15$