When astronomers observe the spectra of distant galaxies, they notice that the hydrogen emission lines are shifted noticeably toward the red end of the visual spectrum, a phenomenon called red shift. red is the lowest frequency of visible light. what does red shift indicate about the movement of the distant galaxies? they are moving away fro us at high speed. they are moving towards us at high speed. they are moving in the same direction as we are. they are motionless, while we are moving toward them at high speed.

A; They are moving away from us at high speed.

ill do it for 100, also this isnt 80 its 40

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 .