Problem:
If f(x)=ax4−bx2+x+5 and f(−3)=2, then f(3)=
Answer Choices:
A. −5
B. −2
C. 1
D. 3
E. 8
Solution:
Since
f(3)f(−3)f(3)−f(−3)=a⋅(3)4=a⋅(−3)4=−b⋅(3)2−b⋅(−3)2+3−36+5+5
Thus, f(3)=f(−3)+6=2+6=8.
Note. For any x,f(x)−f(−x)=2x, so f(x)=f(−x)+2x.
OR
Since
2=f(−3)=81a−9b−3+5
we have
b=9a
Thus
f(3)=81a−9b+3+5=81a−9(9a)+8=8.