Why does time slow down the closer you get to a black hole, I know that time slows down the faster you move through space and the closer you get to the speed of light, but how does being near a black hole slow time down even futher?

Near the black hole, The gravitational pull is so strong and the black hole has a lot of stress energy. This causes the clock to tick slower than usual and due to this , Time slows down to a great extent.

where are the vectors ?

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .