For each of the following functions h(x) and g(x): (i) Determine whether or not an inverse function exists. (ii) If an inverse function exists, then provide a representation of the inverse, h (x) or g (x) (using the same type of representation given for the original function) and justify that the function you have written down really is the inverse. If an inverse function does not exist, then explain why it does not exist. T y = h(x) -3 2 (1) 5 -3 8 -1 5 i) ( ii) (2) y = g(x) X(3) Consider the function h(a) = 3x - 3 ". Are any of the functions g(r) provided below an inverse of h(r)? Explain the reasoning you used and any calculations you performed to answer this question. . g(x) = 25 + 3 8 . g(x) = 8 - 3 . g(x) = 20 - 3 8 . g(x) = 21 + 3 8 . g(x) = 2x + 3 . g(x) = 2x - (4) Consider the function (x) = \\-2 . Are any of the functions j(x) provided below an inverse of k(x)? Explain the reasoning you used and any calculations you performed to answer this question. . j(x) = 3x2 + 1 . i(x) = 3x2 - 1 . j(x) =12 +3 . j(x) = 12 -3 . j(x) = V3x+1 . j(x) = V3x -1 (5) What is the inverse of the function 7 -81 7 3 (6) What is the inverse of the function V35 - 7x