As you learned in part b, a non-burning helium core surrounded by a shell of hydrogen-burning gas characterizes the subgiant stage of stellar evolution. as time goes on, the star continues to evolve, and eventually, it becomes a red giant. rank the stages a star goes through as it evolves from a subgiant into a red giant, from latest to earliest. a) the shell of hydrogen surrounding the star's non-burning helium core ignites. b) pressure in the star's core decreases. c) pressure from the star's hydrogen-burning shell causes the non-burning envelope to expand. d) the star's non-burning helium core starts to contract and heat up. e) the star becomes a red giant. f) the surface of the star becomes brighter and cooler.

E- The star becomes a red giant (LATEST STAGE)

F- The surface of the star becomes brighter and cooler

C- Pressure from the star's hydrogen-burning shell causes the non burning envelope to expand

A- The shell of hydrogen surrounding the star's nonburning helium core ignites.

D- The star's non burning helium core starts to contract and heat up

B- Pressure in the star's core decreases (EARLIEST STAGE)

(A star moves away from the main sequence once its core runs out of hydrogen to fuse into helium. The energy once supplied by hydrogen burning reduces and the core starts to compress under the force of gravity. This contraction allows the core and surrounding layers to heat up. Finally, the hydrogen shell around the core becomes hot enough to ignite hydrogen burning.

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 .