All you have done is to rewrite each composition in a different form. I suspect that there are formulas for f, g, and h that you have overlooked.Niaboc67 said:Homework Statement
1. Find a formula for
(fg)(x) = ?
2. Find a formula for
(ff )(x) = ?
3. Find a formula for the composition below.
g(h(x)) =4. Find a formula for the composition below.
(hg)(x) =
The Attempt at a Solution
1. f(g(x))
2. f(f(x))
3. (g º h)(x)
4. h(g(x))
Why are these incorrect?
A composite function is a mathematical concept where two or more functions are combined to form a new function. The output of one function becomes the input of the next function. The composite function can be thought of as a function within a function.
To find the domain of a composite function, you need to consider the domain of each individual function that makes up the composite function. The domain of the composite function will be the set of all inputs that are valid for all functions in the composite function.
The domain of a composite function is the set of all possible inputs that can be used for the function, while the range is the set of all possible outputs that the function can produce. In other words, the domain is the set of values that can be plugged into the function, and the range is the set of values that the function can output.
Yes, the order of functions can be changed in a composite function. However, the result of the composite function may differ depending on the order in which the functions are composed. It is important to note that the order of functions matters in a composite function.
Composite functions are used in various fields such as physics, engineering, and economics. In physics, composite functions are used to describe the relationship between different physical quantities. In engineering, composite functions are used to model and analyze complex systems. In economics, composite functions are used to model the relationship between different economic variables.