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In the function above, for what values of x is g(x) a real n

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In the function above, for what values of x is g(x) a real n [#permalink] New post 14 May 2019, 01:18
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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) \(x ≥ 3\)
[Reveal] Spoiler: OA

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Re: In the function above, for what values of x is g(x) a real n [#permalink] New post 14 May 2019, 07:27
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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.
Re: In the function above, for what values of x is g(x) a real n   [#permalink] 14 May 2019, 07:27
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In the function above, for what values of x is g(x) a real n

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