1. Answer the following: a. Find the domain: f(x) =+ +; x+4+m (5 marks) b. Let f(x) = 2+4x m+3x find f-1(2). (12 marks) c. If h(x) = vx and k(x) = vm + x, then write (hok) (x) in exponential form. (5 marks) 2. a. Solve the following exponential equation: ( 12 marks) 3* x 53x+m = 160 b. Simplify the following logarithmic expression: ( 10 marks) (log(32) + 10log(x - 3) - log(y)) 3. Most cars get their best gas mileage when traveling at relatively modest speed. The gas mileage M for a certain new car is modeled by the function. M(s) = --s2 + (4 + m)s + (20 + m) , where s is the speed in mi/h and M is measured in mi/gal a. What is the car's best gas mileage, and at what speed is it attained? Justify your answer? (10 marks) b. Sketch the quadratic function showing all steps. (20 marks)4. A bacteria culture starts with 20000 bacteria, and the number doubles every 50 minutes. a. Find a function that models the number of bacteria at time t. (10 marks) b. Find the number of bacterial after two hours. (6 marks) c. After how many minutes will there be (90000 +m) bacteria? (10 marks) ** Note that: the function of bacteria growing is available in many resources, search about it