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Question 881152: Given the functions f(x)=4x-1 g(x)=3-2x^2 h(x)=sq rt (x+5)
Simplify h(g(2k+1)) and state the domain
I have come to sq rt(-8k^2-8k+6), I'm not sure if I should leave it like this, or factor out 2. I need to know the equation and the domain, the domain I would assume wouldnt be the same as the original h(x) domain of x> or equal to -5
Thanks in advance.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! 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
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