SOLUTION: F(x) = x4 - x + 2, then f(-x)

Question 765267: F(x) = x4 - x + 2, then f(-x)
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Given:
(1) f(x) = x^4 - x + 2
The variable x in the name f(x) is called the argument of the function. The algebraic expression on the right side is called the topology of the function whose name is f. You can have any name, e.g. g(y) = y + 4, is a function named g, and argument y and the topology is (y +4).
Return to (1), if we want to evaluate f(x) function with a different argument, say f(2), we simple substitute 2 every place x is given in the topology or
(2) f(2) = 2^4 - 2 + 2 or
(3) f(2) = 16
The stated problem is to find f(-x), so replace x with -x as we did with 2 and get
(4) f(-x) = (-x)^4 - (-x) + 2 Get it? or the answer is
(5) f(-x) = x^4 + x + 2
It's very important to note the error in your statement of the function. You use F(x) and f(x). That's a no no. The name F is not the same as the name f. Case matters! Your statement should be as in (1), NOT F(x).
Using (1), can you give me,
(6) f(a) = ?
Answer
(7) f(a) = a^4 - a + 2
How about
(8) f(y-1) = ?
Answer
(9) f(y-1) = (y-1)^4 - (y-1) + 2 OK?
Thanks for reading, hope you understand a little more about function nomenclature.

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