Find the Domain 37/(k^2-k-30)

Problem

37/(k2−k−30)

Solution

1. Identify the condition for the domain of a rational function. The denominator cannot be equal to zero because division by zero is undefined.

2. Set the denominator equal to zero to find the excluded values of k

k2−k−30=0

3. Factor the quadratic expression by finding two numbers that multiply to −30 and add to −1 These numbers are −6 and 5

(k−6)*(k+5)=0

4. Solve for k by setting each factor to zero.

k−6=0⇒k=6

k+5=0⇒k=−5

5. Exclude these values from the set of all real numbers to define the domain.

Final Answer

Domain: *{[k∈ℝ,k≠6,k≠−5]}

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