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

Question

Select the field of application of the following fraction:

x16 \frac{x}{16}

Video Solution

Solution Steps

00:00 Find the domain of definition
00:03 Domain exists, to ensure we don't divide by 0
00:06 Meaning the denominator in the fraction must be different from 0
00:09 We'll use this formula in our exercise
00:12 We can see that the denominator is different from 0
00:15 Therefore, the domain is valid for all X
00:18 And this is the solution to the question

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