Find the Domain v

Problem

v(t)=(t−1)/(t2−4)

Solution

1. Identify the type of function, which is a rational function.

2. Determine the restriction for the domain, which requires that the denominator cannot be equal to zero.

3. Set the denominator equal to zero to find the excluded values: t2−4=0

4. Solve the equation by factoring the difference of squares: (t−2)*(t+2)=0

5. Find the roots by setting each factor to zero: t=2 and t=−2

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

Final Answer

Domain:{[t∈ℝ,t≠−2,t≠2]}

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