1. The surface area s of a huge beach ball (a sphere) is a function of its radius r and is given by the formula s(r) = 4 r2 the radius of the sphere is increasing with time according to the formula r(t) = 12 t2 measured in seconds, t 0, and r is measured in inches. (a) What is the radius for an inflation time of two seconds, assuming that at time t = 0, the sphere was completely deflated? (Do not forget the measuring unit.) (b) What is the surface area at two seconds? (Do not forget the measuring unit.) (c) Find and interpret (s r)(t). (d) Find (s r)(2) (e) What is the mathematical domain of (s r)(t). (f) What is the physical/applied (real life) domain of (s r)(t), knowing that the sphere (e.g., the beach ball) will explode when its radius exceeds 18 inches. 2. (a) Write the function f(x) = x^2 + 1 as a composition of two (non-identity) functions. (b) Test your answer. 3. (a) How, by looking at the graph of a function, we can tell that the function has an inverse? (b) Apply your prescription to the following graphs and state which one, if any, is invertible. 4. (a) Find the inverse function f 1 ( x ) , given: f ( x )= x 8x (b) find the domain and the range of f (c) find the domain and the range of f 1 (d) Test your answer to Part (a) by resorting to composition of the two functions or graphically. Comment on the result of your test. 5. Find exact solutions for the following equations: 8 x +286=4 6. (a) convert to an exponential equation: (b) convert to a logarithmic equation: logx=12 5 x =60