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

Question

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

Prospect2020 · Accepted Answer

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

KanishkM · Answer

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

celo700 · Answer

what is the meaning of range of a function? How do you approach this problem? Can anybody help...

tannumunu · Answer

Can Any one please help to understand the question?

m1033512 · Answer

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

pierjoejoe · Answer

g(x) is just 1 - something always positive. the set of possible solution of g(x) is x>=2.

for x = 2 --> g(2) = 1
any other value for x that is the set of possible solutions makes the positive element bigger, example: x = 11
g(11) = 1 - sqrt(11-2) = 1-3 = -2 
thus, given x >=2 (the set of all possible solutions of g(x)) --> g(x) (the y value) ranges between -infinity and 1 (included)

Bunuel · Answer

x = 1 is not possible because in that case we’d get a negative number under the square root: √(1 - 2) = √(–1), and even roots of negative numbers are not defined on the GMAT since it only deals with real numbers.

BongBideshini · Answer

g(x) = 1 − \sqrt{(x − 2)} 
Rearranging,
 \sqrt{(x − 2)} = 1 − g(x) 
Since a square root is always nonnegative,
 \sqrt{(x − 2) }≥ 0 
Therefore,
 1 − g(x) ≥ 0
=> g(x) ≤ 1

Answer: (E)

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards