1. (6 marks) For f(x) = Vx2 1 and g(x) = vx - 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)(x) and (gof) (x). 2. (4 marks) Sketch a graph of f(x) - -2(x 41)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( 117 ) 5. (4 marks) Find the exact value of each x E [0, 27) for which sin(2x) - V3 cos(x). 6. If (a) (1 mark) What is the domain of g(x)? (b) (1 mark) Verify (with a sketch and/or short argument) that g is a one-to-one function. (c) (1 mark) Find a formula for the inverse function: that is, find g (x). (d) (1 bonus mark) Find the range of g