- #1
GreenTea09
- 14
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Homework Statement
http://postimg.org/image/48919pl1x/
Homework Equations
f(f(x))= (x^4)-4(x^2)+2,
The Attempt at a Solution
[f(x)]^2=
(x^4)-4(x^2)+2=
[(x-2)^2]-(4x^2)+2
i can't seem to square root (x^4)-4(x^2)+2...
GreenTea09 said:Homework Statement
http://postimg.org/image/48919pl1x/
Homework Equations
f(f(x))= (x^4)-4(x^2)+2,
The Attempt at a Solution
[f(x)]^2=
(x^4)-4(x^2)+2=
[(x-2)^2]-(4x^2)+2
i can't seem to square root (x^4)-4(x^2)+2...
The image link is broken.GreenTea09 said:Homework Statement
http://postimg.org/image/48919pl1x/
No one else pointed this out, so I will. f(f(x)) is not the same as [f(x)]2.GreenTea09 said:Homework Equations
f(f(x))= (x^4)-4(x^2)+2,
The Attempt at a Solution
[f(x)]^2=
That's not relevant here, since you are not being asked to solve for f(x) in the equation [f(x)]2 = ...GreenTea09 said:(x^4)-4(x^2)+2=
[(x-2)^2]-(4x^2)+2
i can't seem to square root (x^4)-4(x^2)+2...
The function F(f(x)) is a composite function, where the output of f(x) is used as the input for the function F. It can also be written as F∘f.
Finding f(x) allows us to have a better understanding of the original function and its behavior. It also allows us to manipulate the function in various ways to solve different problems.
To find f(x), we need to isolate f(x) on one side of the equation and then take the inverse of the function F. This will give us the original function f(x).
The steps to find f(x) in the given equation are as follows:
1. Rewrite the equation as f(x) = F^-1(x^4 - 4x^2 + 2).
2. Use the inverse function of F to isolate f(x).
3. Apply the inverse function to the right side of the equation.
4. Simplify the equation to get the final form of f(x).
The possible values of f(x) depend on the domain of the original function F. In this case, the domain is all real numbers. Therefore, f(x) can take any real number as its input and give an output accordingly.