Problem:
Let f(x)=ax7+bx3+cx−5, where a,b and c are constants. If f(−7)=7, then f(7) equals
Answer Choices:
A. −17
B. −7
C. 14
D. 21
E. not uniquely determined
Solution:
Since f(x)=ax7+bx3+cx−5,
f(−x)=a(−x)7+b(−x)3+c(−x)−5
Therefore, f(x)+f(−x)=−10 and f(7)+f(−7)=−10.
Hence, since f(−7)=7,f(7)=−17.