For each pair of functions, find f ∘g and g ∘f, if they exist. f={(0,-7),(1,2),(2,-1)}

step 1 You first want to find F of G of X. This means you're using the output of G as an input of F. So

For each pair of functions, find f ∘g and g ∘f, if they...

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Key Concepts

Function

A function is a relation that uniquely associates members of one set (called the domain) with members of another set (called the codomain). It is often represented as a set of ordered pairs where each first element is associated with exactly one second element. This ensures that for any input there is one definite output.

Composition of Functions

Function composition is an operation where two functions are combined such that the output of one function becomes the input of the other. It is denoted as (f ? g)(x) = f(g(x)) or (g ? f)(x) = g(f(x)), depending on the order. For the composition to be well-defined, the range of the inner function must be a subset of the domain of the outer function.

Domain and Range Considerations

When composing functions, it is important to check that the values produced by the inner function (its range) are within the set of allowable inputs (the domain) of the outer function. If any value from the inner function does not lie within the domain of the outer function, then the composition is not defined for that element.

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