Final answer:
The inverse of the function F(x) = -x-7 is f⁻¹(x) = -x - 7.
Step-by-step explanation:
To find the inverse of the function F(x) = -x-7, we need to solve for x in terms of y. We start by replacing F(x) with y: y = -x-7. Next, we swap the variables x and y and solve for y: x = -y-7. Now, we isolate y by adding 7 to both sides: x + 7 = -y. Finally, we multiply both sides by -1 to solve for y: -x - 7 = y. Therefore, the inverse of F(x) is f⁻¹(x) = -x - 7.