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What is the range of the function g(x) = 1 - (x - 2)^(1/2) ?

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What is the range of the function g(x) = 1 - (x - 2)^(1/2) ?  [#permalink]

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New post 11 Feb 2019, 01:50
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Question Stats:

54% (01:21) correct 46% (01:28) wrong based on 63 sessions

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Re: What is the range of the function g(x) = 1 - (x - 2)^(1/2) ?  [#permalink]

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New post 11 Feb 2019, 04:38
Bunuel wrote:
What is the range of the function \(g(x) = 1 - \sqrt{x - 2}\) ?


IMO E

\(g(x) = 1 - \sqrt{x - 2}\)

Now we have the answer options as
(A) \(g(x) \geq -2\)

(B) \(g(x) \leq -2\)

(C) \(g(x) \geq 2\)

(D) \(g(x) \geq -1\)

(E) \(g(x) \leq 1\)
g(x) = 1 or g(x) < 1
Only satisfies the expression for this range

x =2, g(2) = 1
x = 3 g(3) = 0
x = 4, g(4) = 0.732
x = 18, g(18) = -3
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Re: What is the range of the function g(x) = 1 - (x - 2)^(1/2) ?  [#permalink]

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New post 05 Apr 2019, 06:22
what is the meaning of range of a function? How do you approach this problem? Can anybody help...
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Re: What is the range of the function g(x) = 1 - (x - 2)^(1/2) ?  [#permalink]

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New post 05 Apr 2019, 13:03
mounicadatti wrote:
what is the meaning of range of a function? How do you approach this problem? Can anybody help...

Can Any one please help to understand the question?
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Re: What is the range of the function g(x) = 1 - (x - 2)^(1/2) ?  [#permalink]

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New post 05 Apr 2019, 14:57
tannumunu wrote:
mounicadatti wrote:
what is the meaning of range of a function? How do you approach this problem? Can anybody help...

Can Any one please help to understand the question?


The range is the set of all possible values of y after substituting in all possible values of x into the function. So in this case, we know that x has to be greater than or equal to 2, because we can't take the square root of a negative number. When x is equal to 2, the radical becomes 0, so y is 1. Now you can try different values of x greater than 2. As the values of x get larger, the result of the function (y) gets more negative.

Therefore, the answer is g(x) is less than or equal to 1
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Re: What is the range of the function g(x) = 1 - (x - 2)^(1/2) ?  [#permalink]

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New post 05 Apr 2019, 19:07
Range means the set of values which g(x) can take when you put different values of x and calculate G(x)

for example x = 3 ,

we get G(3) = 1-√(3-2)
= 1-1= 0

here x can be minimum 2 so we get g(2) = 1

and for any x >= 2

we get 1 - ( some value)

so it will be always less then 1 ( positive or negative)


IMO E

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Re: What is the range of the function g(x) = 1 - (x - 2)^(1/2) ?   [#permalink] 05 Apr 2019, 19:07
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