Functions (operations, compositions, inverses) Review

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What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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What is the notation for a function?

Back

Functions are typically denoted by letters such as f, g, and h, followed by parentheses containing the input variable, e.g., f(x).

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What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.

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How do you find the inverse of a function algebraically?

Back

To find the inverse of a function, swap the x and y variables in the equation and solve for y.

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What is the graphical representation of a function and its inverse?

Back

The graph of a function and its inverse are reflections of each other across the line y = x.

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What is function composition?

Back

Function composition is the process of applying one function to the results of another function, denoted as (f ∘ g)(x) = f(g(x)).

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What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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What is the range of a function?

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The range of a function is the set of all possible output values (y-values) that the function can produce.

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What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input is associated with exactly one output.

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How do you determine if a function is even or odd?

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A function is even if f(-x) = f(x) for all x in the domain, and odd if f(-x) = -f(x) for all x in the domain.