Final answer:
The domain of the function g(t) = (t+2)/(t²+5t+6) is all real numbers except t = -2 and t = -3.
Step-by-step explanation:
The domain of a function is the set of all possible input values that the function can accept. In this case, the function g(t) = (t+2)/(t²+5t+6), the denominator t²+5t+6 cannot be zero because division by zero is undefined. So we need to find the values of t that make the denominator equal to zero:
t²+5t+6 = 0
Factoring the quadratic equation, we get (t+2)(t+3) = 0. So the values of t that make the denominator zero are t = -2 and t = -3. Therefore, the domain of the function g(t) is all real numbers except t = -2 and t = -3.