Explain what dispersion is and how astronomers use this phenomenon to study a star’s light.

Splitting of light in seven different colors showing the complete spectrum is known as dispersion.

Explanation:

The visible part of the complete EM spectrum, visible light, is made up of seven different colors (Acronym: VIBGYOR). When visible light beam is passed through a prism or diffraction grating it splits into 7 different colors, this process is known as dispersion. The band of 7 colors is called as Spectrum of light.

Every element shows a different spectrum. When we study the spectrum of a compound we can get to know which all elements are present inside it. This technique is known as Spectroscopy.

The same technique is used to study the composition of stars. Astronomers study the spectrum of light coming from the stars to know the elements present inside them. Along with that we can also find out the relative motion of stars using the Doppler's effect. We can get to know whether an object is moving towards or away from us by studying its spectrum.

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 .