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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]  14 May 2019, 01:18
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66% (01:03) correct 33% (01:57) wrong based on 3 sessions
$$g(x)= (2x−3)^{\frac{1}{4}} + 1$$

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]  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.
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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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