Identify the Application Context of the Fraction x/16: Mathematical Analysis

Question

Select the domain of the following fraction:

x16 \frac{x}{16}

Video Solution

Solution Steps

00:05 Let's find the domain of definition.
00:08 We need to make sure we don't divide by zero.
00:11 This means the bottom of the fraction cannot be zero.
00:16 We'll use this idea in our exercise.
00:19 Notice that the denominator is not zero.
00:22 So, the domain is valid for any value of X.
00:26 And that solves the problem!

Step-by-Step Solution

Let's examine the given expression:

x16 \frac{x}{16}

As we know, the only restriction that applies to a division operation is division by 0, since no number can be divided into 0 parts, therefore, division by 0 is undefined.

Therefore, when we talk about a fraction, where the dividend (the number being divided) is in the numerator, and the divisor (the number we divide by) is in the denominator, the restriction applies only to the denominator, which must be different from 0,

However in the given expression:

x16 \frac{x}{16}

the denominator is 16 and:

160 16\neq0

Therefore the fraction is well defined and thus the unknown, which is in the numerator, can take any value,

Meaning - the domain (definition range) of the given expression is:

all x

(This means that we can substitute any number for the unknown x and the expression will remain well defined),

Therefore the correct answer is answer B.

Answer

All X All~X