Please answer all with full solutions!! Thank you!

1. (6 marks) For f(x) = vx2 -1 and g(x) = VI -3, determine the subset of the domain of g on which the composition fog is well-defined. What is the domain of go f? Find formulas for (fog)(r) and ( go f) (I) . 2. (4 marks) Sketch a graph of f(x) = -2(r+1)3-6 by using a sequence of transformations of a well-known function. For full points, make sure to describe the various transformations applied to the well-known starting function. 3. (3 marks) A certain bacterial culture grows at a rate proportional to the number of bacteria present. If the culture contains 400 cells initially and 700 after 24 hours, then approximately how many cells will there be after a further 12 hours? 4. (2 marks) Find the exact value of sin( LIT ) 5. (4 marks) Find the exact value of each x E [0, 27) for which sin(2x) = V3 cos(x). 6. If