Find the domain of g(t) = sqrt (3t + 15.)
To find the domain of a function, we need to determine the values of the independent variable, in this case, 't', for which the function is defined.
In the given function g(t) = sqrt(3t + 15), we have a square root function. The square root is defined only for non-negative values. Therefore, for the function to be defined, the expression inside the square root (3t + 15) must be greater than or equal to zero.
We can solve this inequality as follows:
3t + 15 ≥ 0
Subtracting 15 from both sides, we get:
3t ≥ -15
Dividing both sides by 3, we obtain:
t ≥ -5
Therefore, the domain of the function g(t) = sqrt(3t + 15) is all real numbers greater than or equal to -5, represented as [-5, ∞).