Find Domain of PreCalculus Functions Algebraically

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SUMMARY

The domain of the function (3x-1)/((x+3)(x-1)) is defined as all real numbers except for x = -3 and x = 1, which are the values that cause division by zero. This conclusion is reached by identifying the points where the denominator equals zero, thus rendering the function undefined. The algebraic method for determining the domain involves solving for the values that make the denominator zero and excluding them from the domain.

PREREQUISITES
  • Understanding of rational functions
  • Knowledge of algebraic manipulation
  • Familiarity with identifying undefined points in functions
  • Basic concepts of domain and range in mathematics
NEXT STEPS
  • Study how to find the domain of polynomial functions
  • Learn about vertical asymptotes and their relation to domain
  • Explore the concept of piecewise functions and their domains
  • Investigate the impact of transformations on the domain of functions
USEFUL FOR

Students studying precalculus, mathematics educators, and anyone looking to deepen their understanding of function domains and algebraic methods.

disneychannel
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How do you find the domain of functions algebraically?

ex (3x-1)/(x+3)(x-1)
 
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The domain of values for which this function will have a solution is simply all values except the ones that cause division by zero. So for this example if x = -3 or x = 1 there would be division by zero.

So the domain is all real values except x = 1 or x = -3.

Thanks
Matt
 

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