Let the function f : [3,1) -> R be defined by f(z) = (z −3)^2 +5, and

g : R -> R be defined by g(x) = 7 e^x.

(a) Find ran f.

(b) Find g(ran f).

(c) Let B := ran f and C := g(ran f). Write explicitly the expression for (g)^−1(h) for h E C,

and the expression for (f)^−1(x) for x E B.

(d) Write explicitly the expression for (g o f)^−1(h) for h E C.