GMAT Exam > GMAT Questions > If g(x) = -2x2 + 8 and g (-q) = -24, which of...
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If g(x) = -2x2 + 8 and g (-q) = -24, which of the following could be the value of q?
- a)-4
- b)-2
- c)-1
- d)1
- e)2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If g(x) = -2x2 + 8 and g (-q) = -24, which of the following could be t...
Given:
- g(x) = -2x^2 + 8
- g(-q) = -24
To find:
- Possible values of q
Solution:
Substitute -q in place of x in g(x) to get g(-q)
g(-q) = -2(-q)^2 + 8
g(-q) = -2q^2 + 8
Given that g(-q) = -24, we can set up the equation:
-2q^2 + 8 = -24
Simplifying, we get:
-2q^2 = -32
Dividing by -2, we get:
q^2 = 16
Taking the square root of both sides, we get:
q = ±4
Therefore, the possible values of q are -4 and 4.
Option A (-4) is the correct answer.
- g(x) = -2x^2 + 8
- g(-q) = -24
To find:
- Possible values of q
Solution:
Substitute -q in place of x in g(x) to get g(-q)
g(-q) = -2(-q)^2 + 8
g(-q) = -2q^2 + 8
Given that g(-q) = -24, we can set up the equation:
-2q^2 + 8 = -24
Simplifying, we get:
-2q^2 = -32
Dividing by -2, we get:
q^2 = 16
Taking the square root of both sides, we get:
q = ±4
Therefore, the possible values of q are -4 and 4.
Option A (-4) is the correct answer.
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Community Answer
If g(x) = -2x2 + 8 and g (-q) = -24, which of the following could be t...
To find the value of q that satisfies the given conditions, we can substitute -q into the expression for g(x) and equate it to the given value of g(-q).
Given: g(x) = -2x^2 + 8
We need to find the value of q that satisfies g(-q) = -24.
1. Substituting -q into the expression for g(x):
g(-q) = -2(-q)^2 + 8
2. Simplifying the expression:
g(-q) = -2q^2 + 8
3. Equating g(-q) to -24:
-2q^2 + 8 = -24
4. Solving for q:
-2q^2 = -32
q^2 = 16
q = ±√16
q = ±4
Therefore, the possible values for q are 4 and -4. However, since we are looking for the value of q that satisfies g(-q) = -24, we need to substitute these values into the expression for g(x) and check if g(-q) equals -24.
1. Substituting q = 4:
g(-4) = -2(-4)^2 + 8
g(-4) = -32 + 8
g(-4) = -24
2. Substituting q = -4:
g(4) = -2(4)^2 + 8
g(4) = -32 + 8
g(4) = -24
Both values of q satisfy g(-q) = -24, so the possible value of q is -4. Therefore, the correct answer is option A, -4.
Given: g(x) = -2x^2 + 8
We need to find the value of q that satisfies g(-q) = -24.
1. Substituting -q into the expression for g(x):
g(-q) = -2(-q)^2 + 8
2. Simplifying the expression:
g(-q) = -2q^2 + 8
3. Equating g(-q) to -24:
-2q^2 + 8 = -24
4. Solving for q:
-2q^2 = -32
q^2 = 16
q = ±√16
q = ±4
Therefore, the possible values for q are 4 and -4. However, since we are looking for the value of q that satisfies g(-q) = -24, we need to substitute these values into the expression for g(x) and check if g(-q) equals -24.
1. Substituting q = 4:
g(-4) = -2(-4)^2 + 8
g(-4) = -32 + 8
g(-4) = -24
2. Substituting q = -4:
g(4) = -2(4)^2 + 8
g(4) = -32 + 8
g(4) = -24
Both values of q satisfy g(-q) = -24, so the possible value of q is -4. Therefore, the correct answer is option A, -4.
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