SOLUTION: Suppose f(x)=ax^4+bx^2+x+5, where a and b are constants. Find f(4) if f(-4)=3

Question 995514: Suppose f(x)=ax^4+bx^2+x+5, where a and b are constants. Find f(4) if f(-4)=3
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
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Suppose f(x)=ax^4+bx^2+x+5, where a and b are constants. Find f(4) if f(-4)=3.
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Let us write the fact that f(-4) = 3.
Simply substitute x = -4 into the given polynomial. You will have

f(-4) = = .

Simplify it, taking into account that = and = . You will have

f(-4) = = .         (1)

Now express f(4). Simply substitute x = 4 into the given polynomial. You will get

f(4) = .                     (2)

Now compare expressions (1) and (2). They are almost identical. The difference is in linear terms (-4) in (1) and 4 in (2).
Hence, f(4) is in 8 units greater than f(-4). It means that f(4) = f(-4) + 8 = 3 + 8 = 11.

Answer. f(4) = 11.

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