Question 881152
Simplify h(g(2k+1))
g(2k+1) = 3 - 2(2k+1)^2 = 3 - 2*(4k^2 + 4k + 1) = 3 - 8k^2 - 8k -2
g(2k+1) = -8k^2 - 8k + 1
h(g(2k+1)) = square root (-8k^2 - 8k + 1 + 5)
h(g(2k+1)) = square root (-8k^2 - 8k + 6)
h(g(2k+1)) = square root ((4k-2)*(-2k-3))
domain is k < 1/2 and k > -3/2 or the interval (-3/2, 1/2), this ensures that we will be taking the square root of a positive number