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anonymous
 3 years ago
Find the domain and range of:
f(x)=18sqrt(x)17
anonymous
 3 years ago
Find the domain and range of: f(x)=18sqrt(x)17

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0D={x: where x belong to R and x >=17} R={ y>=0}

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so, would it be 18x17>=0? and solve?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0is this your function: \(\large f(x)=18\sqrt{x}17 \)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1346012919057:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the domain of f is all the x values that give f(x) a real value.... so looking at the function, the function will not give you a real number when x is less than 0....

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so the actual question in finding the domain is "what x values is \(\large \sqrt x =real\) number

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0would I do.. 18x17<0 and solve?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0root of x is always larger than 0

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0You're just looking to be sure that what's under the root does not go negative. So x cannot be negative. Since the smallest value of x is 0 (because of the domain), then the range's minimum value will happen when x is 0. (So plug in 0 for x, and see what y is). The upper limit of the function will go on forever.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0You got it, that's the minimum of the range. As x gets bigger and bigger, there is no limit, it just grows and grows forever.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so.. [17,infinity) ?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0That is your range, yes.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0how do I find the domain with this function?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Well, as we talked about earlier, the domain would be anything that is a "no no". You have a square root, and here, you cannot take the square root of a negative number, as it has no real solutions.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0anything that is NOT a "nono", sorry ;]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0No, you simply have sqrt(x), since you cannot take the square root of a negative number, we know that x MUST be greater than or equal to 0.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1346014535907:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0We're looking for x's that might make the equation undefined. That's what it means to find the domain. The only thing in this equation that can become undefined (or have no real solutions) is the square root. Which can't be negative.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so x is all real numbers that are positive then?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Yep, or in other words x >= 0

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0how do I put that into interval notation though? [0,inf)
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