Use the hr diagram below to answer the question. labeled hr diagram. the main sequence slopes from the upper-left of the diagram, which is blue, to the bottom-left of the diagram, which is red-orange. white dwarfs cluster at the bottom of the diagram, in the light blue section. red giants cluster in the middle of the diagram, in the orange-red section. red supergiants cluster at the top of the diagram, in the orange-red section. what can be concluded about the initial mass of a blue main sequence star compared to a red main sequence star?

Blue stars are young stars. Their initial mass is very high as compared to the red main sequence stars. The mass fuels the fusion reaction inside the star.The red main sequence stars are towards the end of their lives. The fuel is used up. There is no more fusion reaction going on. The outer layer expands. So, these red giants and super-giants are massive in volume not in mass.

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 .