One-to-One Function

Question

The function f(x)=(x+4)^2 is not one-to-one. Choose a largest possible domain containing the number 100 so that the function restricted to the domain is one-to-one. 

The largest possible domain is ?

the inverse function is g(x)=?

Is the largest possible domain (-infinity, +infinity)

Answer 1

The largest possible domain cannot be (-∞,∞). With that domain, it would hit 2 points at the same time and fail the horizontal line test. This parabola is shifted 4 units to the left. So the vertex is (-4,0). To make it one to one, you either have to take off the left or right side. Since you need to include 100, keep the right side so the largest domain would be [-4,∞)