If f(x)=ax^4-bx^2+x+5 and f(-3)=2, then f(3)=

1995 AMC 12 Problem 14

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14.

f(x)=ax^4-bx^2+x+5

and

f(-3)=2,

then

f(3)=

-5

-2

1

3

8

The terms with even powers are unchanged when

x

is replaced by

-x

Compare

f(3)

and

f(-3)

without solving for

a

b

The even-power terms and constant are the same at

3

and

-3,

while the linear term changes from

-3

3.

Hence

f(3)-f(-3)=6,

f(3)=2+6=8.

Thus the correct answer is E.