domain.......

Question

when determining the domain of a function that has a root as the numerator and a quadratic function as a denominator, do I need to solve just the latter one or both?

when determining the domain of a function that has a root as the numerator and a quadratic function as a denominator, do I need to solve just the latter one or both?

Answer 1

You need to solve for the zeroes in the denominator. Be careful- if you factor out the numerator and you can cancel out something in the numerator and denominator, it is still a zero!

Answer 2

You have a root in the numerator.

This means the discriminant, the part under the root, must be

greater than or equal to zero so you set

 

discrimant ≥ 0 and solve that for the restrictions on the numerator

 

Example:  If the numerator is √(x-4) then x-4≥0 so x≥4 is a restriction.

 

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As for the denominator, we cannot divide by zero so

Solve the quadratic on the bottom by setting it equal to zero

and either factor or use the quadratic equation to find out

what values of the variable in the denominator are restricted.