Final answer:
To determine the value of k for which the function g is continuous at x=-3, we need to check if the left and right limits of g at x=-3 are equal to the value of g at x=-3. The value of k that satisfies this condition is -1.
Step-by-step explanation:
To determine the value of k for which the function g is continuous at x=-3, we need to check if the left and right limits of g at x=-3 are equal to the value of g at x=-3. Let's first find the left and right limits.
Left Limit: lim(x → -3-) g(x) = lim(x → -3-) (k + 2) = k + 2.
Right Limit: lim(x → -3+) g(x) = lim(x → -3+) (√[x+7] - 1) = (√[-3+7] - 1) = (√4 - 1) = 2 - 1 = 1.
For g to be continuous at x=-3, the left limit and right limit should be equal to the value of g at x=-3. Therefore, we have the equation k + 2 = 1. Solving this equation gives us k = -1.