What is the result of three compositions of the function f at -1?

spartas · 2015-10-03T13:34:54+00:00

IF f(X)={x2, X>3 ; 3X+4, 0<X<3 ; X3+2 , X<0 } find (f°f°f)(-1) p.s the answer is 49! i don't know how this f(x) includes three terms x2 , 3x+4 and x3+2 And which term i need to use for the (f°f°f)(-1)

MHB
Thread starter spartas
Start date Oct 3, 2015
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Composition Functions

In summary, the composition of functions is a mathematical operation where the output of one function is used as the input for another function, resulting in a new composite function. It is expressed using the notation (f ∘ g)(x) and follows a right to left order of operations. Not all functions can be composed; the output of the first function must be in the domain of the second function and vice versa. The purpose of composition of functions is to create a new function with different properties and characteristics, making it useful for simplifying complex functions, transforming functions, and solving equations.

Oct 3, 2015

spartas

IF f(X)={x², X>3 ; 3X+4, 0<X<3 ; X³+2 , X<0 }

find (f°f°f)(-1)

p.s the answer is 49! i don't know how this f(x) includes three terms x² , 3x+4 and x³+2 And which term i need to use for the (f°f°f)(-1)

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Oct 3, 2015

Greg

Gold Member

MHB

f(-1) = 1, f(1) = 7, f(7) = 49

Related to What is the result of three compositions of the function f at -1?

1. What is the definition of composition of functions?

The composition of functions is a mathematical operation where the output of one function is used as the input for another function. This results in a new function, called the composite function, that combines the operations of the two individual functions.

2. How is composition of functions expressed?

Composition of functions is expressed using the notation (f ∘ g)(x), where f and g are the two functions being composed and x is the input value. This can also be written as f(g(x)) or g(f(x)).

3. What is the order of operations in composition of functions?

The order of operations in composition of functions is right to left. This means that the function on the right will be applied first, and its output will be used as the input for the function on the left. For example, in the composition (f ∘ g)(x), g will be applied first and then f will be applied to the output of g(x).

4. Can any two functions be composed?

No, not all functions can be composed. The output of the first function must be in the domain of the second function in order for composition to be possible. Additionally, the output of the second function must be in the range of the first function. If these conditions are not met, the composition will not be valid.

5. What is the purpose of composition of functions?

The purpose of composition of functions is to create a new function with different properties and characteristics than the original functions. This can be useful in simplifying complex functions, transforming functions, and solving equations. It also allows for a more efficient way to represent mathematical operations.