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Domain

from class:

Algebra and Trigonometry

Definition

The domain of a function is the set of all possible input values (typically $x$-values) for which the function is defined. It represents the range of values over which the function can be evaluated.

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5 Must Know Facts For Your Next Test

  1. The domain excludes any values that cause division by zero or result in a negative number under an even root.
  2. For trigonometric functions, restrictions include angles that make the denominator zero (e.g., $\tan(x)$ at $x = \frac{\pi}{2} + k\pi$).
  3. The domain of composite functions depends on the domains of both individual functions; it must satisfy both.
  4. When determining the domain from a graph, look for all possible horizontal extents where the function produces valid outputs.
  5. For inverse trigonometric functions like $\arcsin(x)$ and $\arccos(x)$, their domains are restricted to $[-1, 1]$.

Review Questions

  • What is the domain of $f(x) = \frac{1}{x-2}$?
  • How do you determine the domain of a composite function $f(g(x))$?
  • What are the domain restrictions for $\arctan(x)$?
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