Jpyhsics said:Homework Statement
f(x)= x/(1+x)
What is f(f(x)) and what is its domain.
2. The attempt at a solution
I found f(f(x))= x/(1+2x)
and the domain: (-∞,-1/2)∪(-1/2,∞) , but it is saying that I have the wrong domain. What mistake have I made?
My process for finding domain:
1. Find the domain of f : x≠-1
2. Use the definition D: {x∈(-∞,-1)∪(-1,∞) | (x/1+x) ≠ -1}
3. Find the ∩ (intersection) for the two domains.
Oh I see! Its undefined!PeroK said:What is ##f(f(-1)##?
Jpyhsics said:Oh I see! Its undefined!
So I guess my domain should be (-∞,-1)∪(-1,-1/2)∪(-1/2,∞)
Thank You!
The composition of functions is a mathematical operation where two functions are combined to create a new function. It is denoted as (f ∘ g)(x) and read as "f composed with g of x". The output of one function is used as the input for the other function.
The domain of a composite function is the set of all values that can be input into the initial function and produce a valid output that can be used as an input for the second function. The range of a composite function is the set of all values that can be output from the final function.
The composition of functions is evaluated by plugging the inner function into the outer function. For example, if f(x) = 3x and g(x) = x + 2, then (f ∘ g)(x) = f(g(x)) = 3(x + 2) = 3x + 6. The inner function (g(x)) is substituted into the outer function (f(x)), and then the resulting expression is simplified.
Composition of functions combines two functions to create a new function, whereas multiplication of functions multiplies two functions to create a new function. In composition, the output of one function becomes the input of the other, while in multiplication, the two functions are multiplied together.
Composition of functions is used in various fields such as engineering, economics, and computer science. It can be used to model complex systems, optimize processes, and analyze data. For example, in economics, the demand curve for a product can be represented as a composition of two functions - one for the price and one for the quantity demanded.