Fill in the blanks with the appropriate word, phrase, or...

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list. $$\begin{array}{lllll}\text { inverse } & \text { domain } & \text { horizontal } & x & f(x) \\\text { vertical } & \text { range } & \text { one-to-one } & \text { composition } & y\end{array}.$$ A function is a __________ function if each element in the range corresponds to exactly one element in the domain.

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$$\begin{array}{lllll}\text { inverse } & \text { domain } & \text { horizontal } & x & f(x) \\\text { vertical } & \text { range } & \text { one-to-one } & \text { composition } & y\end{array}.$$
A function is a __________ function if each element in the range corresponds to exactly one element in the domain.

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Key Concepts

Inverse Function

An inverse function essentially reverses the mapping of a function, meaning it takes outputs as inputs and recovers the original inputs. For an inverse function to exist, the original function must be one-to-one so that each output corresponds to exactly one input.

One-to-One Function

A one-to-one function, also known as an injective function, is one in which each element of the function's domain maps to a unique element in the range, meaning no two distinct inputs share the same output. This property is essential when considering the existence of an inverse function.

Domain

The domain of a function is the complete set of possible input values for which the function is defined. It represents all the elements that can be substituted into the function to produce an output.

Range

The range of a function is the set of all possible outputs or values that the function can produce. It includes every result obtained by applying the function to elements of its domain.

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