GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Dec 2019, 10:53

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59725
What is the range of the function g(x) = 1 - (x - 2)^(1/2) ?  [#permalink]

### Show Tags

11 Feb 2019, 01:50
00:00

Difficulty:

45% (medium)

Question Stats:

55% (01:19) correct 45% (01:27) wrong based on 96 sessions

### HideShow timer Statistics

What is the range of the function $$g(x) = 1 - \sqrt{x - 2}$$ ?

(A) $$g(x) \geq -2$$

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

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

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

(E) $$g(x) \leq 1$$

_________________
Director
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: What is the range of the function g(x) = 1 - (x - 2)^(1/2) ?  [#permalink]

### Show Tags

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
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Intern
Joined: 22 May 2018
Posts: 49
Re: What is the range of the function g(x) = 1 - (x - 2)^(1/2) ?  [#permalink]

### Show Tags

05 Apr 2019, 06:22
what is the meaning of range of a function? How do you approach this problem? Can anybody help...
Intern
Joined: 15 Nov 2017
Posts: 11
Re: What is the range of the function g(x) = 1 - (x - 2)^(1/2) ?  [#permalink]

### Show Tags

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

Intern
Joined: 23 Feb 2019
Posts: 8
Re: What is the range of the function g(x) = 1 - (x - 2)^(1/2) ?  [#permalink]

### Show Tags

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

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
Senior Manager
Joined: 25 Feb 2019
Posts: 335
Re: What is the range of the function g(x) = 1 - (x - 2)^(1/2) ?  [#permalink]

### Show Tags

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

Posted from my mobile device
Re: What is the range of the function g(x) = 1 - (x - 2)^(1/2) ?   [#permalink] 05 Apr 2019, 19:07
Display posts from previous: Sort by