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anonymous
 4 years ago
find the domain and range g(z)= 1 over square root 4z square
anonymous
 4 years ago
find the domain and range g(z)= 1 over square root 4z square

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0find the value of z that will make the equation undefined... sq root (4z^2) = 0 4  z^2 = 0 4 = z^2 z = +/ 2 so...your domain is all values of x except for 2 and 2...which can be written as...(inf, 2)U(2, inf) as for the range...cross multiply. y(sq root 4z^2) = 1 4  z^2 = 1/y^2 z^2 = 4  1/y^2 z^2 = (4y^2  1 )/y^2 get the sq root z = sq root (2y +1)(2y1)/y anyways...your range is everything below and equal to zero...so your range is (inf, 0)U(0, inf)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0how you throw away the square root to find range?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0y(sq root 4z^2) = 1 divide both sides by y sq root 4z^2 = 1/y square both sides... 4z^2 = 1/y^2

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0hmmm \[\frac{1}{\sqrt{4z^2}}\] need \[4z^2>0\] \[(2z)(2+z)>0\] i think this is \[(2,2)\] as the domain

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0it is a square root right?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0is z a real variable?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ooooooooh range i see ok that would be \[(\frac{1}{2},\infty)\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0reason as follows. this beast can get as large as possible by making the denominator small, that is make x close to 2 or 2 the denominator is largest when x is 0, and when x is 0 you get \[\frac{1}{\sqrt{4}}=\frac{1}{2}\] so that is the minimum value of the function

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so to be more precise, range is \[[\frac{1}{2},\infty)\] or \[\frac{1}{2}\leq y<\infty\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0actly which answer the correct one??? im blur

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[g(z)=\frac{1}{\sqrt{4z^2}}\] Domain \[(2,2)\] Range \[[\frac{1}{2},\infty)\]
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