Let f : R → R be the function with formula f(x) = x 3−x 2 = x 2 (x−1). (i) Graph this function (figure out where it is zero, positive and negative). (ii) (a) Find (nonempty) sets X, Y ⊂ R so that the restriction f|X is a bijection from X onto Y . (b) Is there a maximal choice for X? i. e. is there a set X with this property and also such that no set larger that X has this property? If there is, is it unique? (c) Is there a maximal choice for Y ? If there is, is that unique?

You eat 8 strawberries and your friend eats 12 strawberries from a bowl. there are 20 strawberries left. which equation and solution give the original number of strawberries?

If f(x) = 4x – 3 and g(x) = 8x + 2, find each function value a. f[g(3)] b. g[f(5)] c. g{f[g(-4)]}

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?