Pure Mathematics

lu. Assignment 1 QP. PM2.1 Hiwik Assignment Tasks Note: m is the last digit of your college ID. Show all steps 1. Answer the following: a. Find the domain: f(x) =*+ ***+x+z+m. (5 marks) 2+4x b. Let f(x) = m-2x findf-‘(x). (10 marks) c. If f(x) = Vx and g(x) = m + x, then find (fog)(x) in simplest form. (5 marks) 2. 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($) = -52 + (3 + m)s + (31 + 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 manually showing all steps. (20 marks) 3. (6 marks) a. Expand the logarithmic expression logs x((m+4) -5x) VX-X (10 marks) b. Solve the following equations: i. 22/logs (x-m) = 1 16 ii. e4x + 4e2x – 21 = 0 (8 marks) MEC_AMO TEM_035_02 Page 2 Pure Mathematics (FNDM PM2.1) – Summer – 21 – CW1 (Assignment) -ALL-QP 4. A culture starts with 10000 bacteria, and the number doubles every 40 minutes. a. Find a function that models the number of bacteria at time t. (9 marks) b. Find the number of bacterial after one hour. (4 marks) c. After how many minutes will there be (50000+m) bacteria? (8 marks) d. Sketch a graph of the number of bacterial at time t. (5 marks) Rules & Regulations: Explain with suitable diamewhereverdDas must be drawn using suitable software or hy nencil
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