You can put this solution on YOUR website! .
Suppose f(x)=ax^4+bx^2+x+5, where a and b are constants. Find f(4) if f(-4)=3.
-------------------------------------------------------------------------
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.
