Discuss the relationship between functions, their inverses, and the results of function operations. choose one type of function operation (composition, sum or difference, product or quotient) and explore the related question. you may use equations, diagrams, or graphs to organize and present your thoughts.
choose any two specific functions that have inverses. use your chosen functions to answer any one of the following questions:
if the inverses of two functions are both functions, will the inverse of the composite
function made by the original functions also be a function?
if the inverses of two functions are both functions, will the inverse of the sum or difference of the original functions also be a function?
if the inverses of two functions are both functions, will the inverse of the product or quotient of the original functions also be a function?

Submarines control how much they float or sink in the ocean by changing the volume of air and water contained in large ballast tanks. when the tanks are completely full of water, the submarine increases its overall mass and sinks down to the bottom. when the tanks are completely full of air, the submarine reduces its overall mass and floats to the surface. depending on the density of the seawater surrounding the submarine, it will pump seawater in or out of the tanks in order to achieve the same overall density as the sea water and float neutrally in the water. the volume of the submarine never changes. when the tanks are completely full of water, a submarine with a volume of 7.8\times10^3\text{ m}^37.8×10 3 m 3 7, point, 8, times, 10, start superscript, 3, end superscript, space, m, start superscript, 3, end superscript has a total mass of 8\times10^6\text{ kg}8×10 6 kg8, times, 10, start superscript, 6, end superscript, space, k, g. the density of the seawater is 10^3\text{ kg/m}^310 3 kg/m 3 10, start superscript, 3, end superscript, space, k, g, slash, m, start superscript, 3, end superscript. to make that submarine float neutrally, and neither float nor sink in the ocean, what volume of water does that submarine need to subtract from its tanks?