Let f(x)=ax7+bx3+cx−5, where a, b, and c are constants.
If f(−7)=7, then what is f(7)?
−17
−7
14
21
not uniquely determined
Solution
Since f(x) = ax7 + bx3 + cx –5, and f(−7)=7 then
f(−7)7777= a(−7)7 + b(−7)3 + c(−7)–5,= a(−7)7 + b(−7)3 + c(−7)−5,=−a77 − b73 − c(7)−5=−(a77−b73−c(7)−5)−10=−f(7)−10.
So f(7)=−10−7=−17. The answer is (a).