Restricted domain

Definition

A restricted domain is a subset of the original domain of a function, chosen to make the function one-to-one. This is essential for finding an inverse function.

5 Must Know Facts For Your Next Test

1. Restricting the domain ensures that each $y$-value corresponds to exactly one $x$-value.
2. For a function to have an inverse, it must be injective (one-to-one).
3. Common functions requiring domain restrictions include quadratic and trigonometric functions.
4. Graphically, restricting the domain may involve selecting a portion where the function passes the Horizontal Line Test.
5. The restricted domain often depends on the context or specific problem requirements.

Review Questions

• Why is it necessary to restrict the domain of some functions?
• How do you determine an appropriate restricted domain for a function?
• $\text{If } f(x) = x^2 \text{, what could be a possible restricted domain?}$

Related terms

Inverse Function:

A function that reverses another function such that if $f(a) = b$, then its inverse $f^{-1}(b) = a$.

Horizontal Line Test:

A graphical method to determine if a function is one-to-one; if any horizontal line intersects the graph more than once, it is not one-to-one.

Injective Function: \text{A function where each element of the range is mapped by exactly one element of its domain.}