Home of x x x^{x}

Algebra Level 5

Which of the following indicates the domain of x x x^{x} ?

A) { x x = 2 p + 1 2 q , p , q N } ( 0 , ) B) R { x x = 2 p + 1 2 q , p , q N } C) { x x = p 2 q + 1 , p , q N } ( 0 , ) D) ( 0 , ) \begin{array}{c}\text{A)} & \{ x | x = - \frac{ 2p+1 } { 2q} , p, q \in \mathbb{N} \} \cup ( 0, \infty) \\ \text{B)} & \mathbb{R} - \{ x | x = - \frac{ 2p+1 } { 2q} , p, q \in \mathbb{N} \} \\ \text{C)} & \{x|x=-\frac {p}{2q+1},p,q \in \mathbb {N}\}\cup (0,\infty) \\ \text{D)} & (0,\infty) \end{array}

A B C D None of these

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1 solution

Prince Loomba
Nov 1, 2016

All the negative numbers that have odd denominator can be in domain but those irrational or with even denominator are not defined, as square root is not defined(real) for negative numbers. And all the positive numbers are obviously in the domain. The option that satisfies this is C.

Is B wrong because zero is included in the domain...is there another reason ? -Great question by the way!

Abdo Reda - 2 years, 11 months ago

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Yes the main reason is that only. And thanks^^

Prince Loomba - 2 years, 9 months ago

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