please ignore the AI part on the final question , and use communication skills in explaining the answer

For full credit, ensure you show all your work and explain your reasoning. Simply stating the final answer for any of the following questions will not result in full credit. Your solution should be well written and concise. Each question will be evaluated for communication skills using the communication rubric in the Course Outline and as posted on OWL - this means that in addition to the points indicated with each question, three (3) additional points will awarded with regards to communication. You are welcome to work with one (1) other peer in our section of calculus, and sub- mit one problem set as a pair. Please ensure when submitting to Gradescope that you have identified both yourself and your partner. Failure to identify both students may result in the loss of points. Points for this Problem Set: 22 mathematical points + 18 communication points = 40 total points 1. (+ communication rubric) Consider the functions f(x) = 2 2r - 8 and g(x) = 1+ 3r (a) (1 point) What is the domain of f(x)? What is the domain of g(r)? (b) (2 points) Determine f(g(r)), and its domain. (c) (2 points) Determine g(f(r)), and its domain. 2. (4 points + c.r.) Consider the functions r(t) = 3- =(t-1)3 and $(0) = 3 - =(t -1)'. Do both of these functions have a corresponding inverse function? If not, use your knowledge of a certain test to demonstrate no inverse function would exist; if so, use algebra to determine the corresponding inverse function. 3. (4 points + c.r.) Determine the value of tan (). Show all your work, and ensure you identify which identities you use (if any). 4. (2 points + c.r.) Determine the value of sin (cos-1 ())-5. (+ c.r.) The Ebbinghaus forgetting curve is a basic model that has been used to approximate forgetting. The basic model is given by the exponential decay equation, R() = Roe-1/s where R(t) is retrievability rating at time t, Ro is the intrinsic retrievability rating of the person, and S is the stability of memory. Your answers for all parts are okay (and encouraged) to have In functions. (a) (2 points) Suppose that a patient has an intrinsic retrievability rating of Ro = 3 (some weird test has determined this), and they are likely to lose exactly half of their retrievability after 1 hour (think about what this means... what should R(1) be equal to?). What is this person's stability of memory? (b) (2 points) How long would it take the same person to have a retrievability rating of 1/6? An exact answer would be preferred, but you can give a decimal response (with four decimals) if desired. (c) (1 point) Suggest an idea how this person (maybe even yourself) could improve their stability of memory. 6. (2 points + cr.) { AI Question } Use some Al tool to solve the following expression for r: log(3x - 4) = log(I - 2) - What does the Al determine the solution for r is? Does this solution make sense? Explain. Include some short critique of the solution the AI system gives - what does it miss? does it explain the solution well? etc. For full points, please include a screengrab of your prompt given to the Al system and the AI system's response