Find the domain of g(t) = sqrt (3t + 15.)
To find the domain of the function g(t) = sqrt(3t + 15), we need to determine which values of t make the expression inside the square root non-negative. In other words, we need to find the values of t that make the radicand (3t + 15) greater than or equal to zero.
To solve this, we set the radicand equal to zero and solve for t:
3t + 15 >= 0
Subtracting 15 from both sides:
3t >= -15
Dividing both sides by 3 (since 3 is a positive number):
t >= -5
So, the values of t that satisfy the inequality are t greater than or equal to -5. Therefore, the domain of the function g(t) is the set of all real numbers greater than or equal to -5, expressed in interval notation as (-5, ∞).