Final answer:
To find the range of the inverse of the function f(x)= sqrt(x+3)+5 for (x > -3), we switch the roles of x and y, solve for y, and find that the range of the inverse function is (-∞, ∞).
Step-by-step explanation:
To find the range of the inverse of the function f(x)= sqrt(x+3)+5 for (x > -3), we need to first find the inverse of the function. To do this, we can switch the roles of x and y in the function, and then solve for y. So we have: x = sqrt(y+3)+5. Now we can solve for y:
y = (x-5)^2 - 3.
The range of the inverse function is all possible values of y, which in this case is (-∞, ∞).