This is 11th grade Advanced Algebra C&C. Please show complete show work with step by step explanation so I will understand. I really need help asap.

30. Let f(x) = 15(4)*-2 + 7. Find the inverse of f(x) and use it to find x such that f(x) = 247. Show your work. 31. Identify and correct the error that a student made when solving the equation 7(10)0 25x =5375. 7(10)0.25x = 5375 10025x 5375 7 log 100.25x = log- 5375 7 5375 0.25x log 10 = log - 7 0.25x = log 5375 -log 7 0.25x =log 5368 X = 4 log 5368 x = 14.92 32. Find the inverse of f(x) = Vx-2. Show your work. Also, describe how the domain and range of f(x) compare to the domain and range of its inverse. What are the domain and range of the inverse? 33. The function P(t) = 50(2)025 models the population P of a certain type of bacteria after t hours. How long does it take the initial population to double? A)0.25 hour (B)2 hours C4 hours 50 hours 34. The function GDP(1) = 0.504(1.18) models the gross domestic product GDP, in trillions of dollars, as a function of the time t, in years, of a nation from 2002 to 2011. What is the annual percentage increase in the gross domestic product during this period? A 0.18% (B) 0.504% C 1.18% D 18%35. Consider the function f(x) = 4x2 + 4x - 15. a. Factor the expression 4x2 + 4x - 15. What are the zeros of f(x)? b. What are the coordinates of the vertex of f(x)? Is the vertex the maximum or minimum value of the function? Explain. 36. Which of these functions describe exponential growth? A f(t) = 1.25' B f(t) = 2(0.93)0.5 f(t) = 3(1.07)3 D f(t) = 18(0.85)' E f(t) = 0.5(1.05) F ff) = 3(1.71)5 G f(t) = 0.682 A f(t) = 8(1.56)14 37. The graph of a logarithmic function is shown. What is the domain of the function? f(x) A x25 B x> 5 Dy