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In the function above, for what values of x is g(x) a real n
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14 May 2019, 01:18
14 May 2019, 01:18
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Expert Reply
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Question Stats:
75% (00:57) correct
25% (01:09) wrong based on 16 sessions
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\(g(x)= (2x−3)^{\frac{1}{4}} + 1\)
In the function above, for what values of x is g(x) a real number?
(A) \(x ≥ 0\)
(B) \(x ≥ \frac{1}{2}\)
(C) \(x ≥ \frac{3}{2}\)
(D) \(x ≥ 2\)
(E) \(x ≥ 3\)
In the function above, for what values of x is g(x) a real number?
(A) \(x ≥ 0\)
(B) \(x ≥ \frac{1}{2}\)
(C) \(x ≥ \frac{3}{2}\)
(D) \(x ≥ 2\)
(E) \(x ≥ 3\)
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GMAT 1: 770 Q51 V44
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Re: In the function above, for what values of x is g(x) a real n
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14 May 2019, 07:27
14 May 2019, 07:27
1
Expert Reply
First remember that raising a quantity to a fractional exponent is equivalent to taking the radical of the number in the exponent's denominator.
Therefore, we can rewrite the expression as g(x) = ∜(2x-3) + 1
Thus, because taking an even root of any negative results in a non-real or imaginary number, we know that 2x - 3 must be ≥ 0.
Solve the inequality by adding 3 to each side and then dividing by 2 to find that the domain of g(x) is x ≥ 3/2, which is choice C.
Therefore, we can rewrite the expression as g(x) = ∜(2x-3) + 1
Thus, because taking an even root of any negative results in a non-real or imaginary number, we know that 2x - 3 must be ≥ 0.
Solve the inequality by adding 3 to each side and then dividing by 2 to find that the domain of g(x) is x ≥ 3/2, which is choice C.
Re: In the function above, for what values of x is g(x) a real n
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11 Sep 2021, 16:01
11 Sep 2021, 16:01
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