It is a function because in a function the x's do not repeat. So since there are no two numbers in the x column that are the same, yes it is a function.

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=Simplify%3A%20%20%5Cfrac%7B%20%7Bx%7D%5E%7Ba%20%2B%20b%7D%20.%20%7Bx%7D%5E%7Bb%20%2B%20c%7D%20

kozerog [31]

Step-by-step explanation:

$\bf \underline{Solution-} \\$

We have to simplify the given expression.

$\rm = \dfrac{ {x}^{a + b} \cdot {x}^{b + c} \cdot {x}^{c + a} }{ {x}^{a} \cdot {x}^{b} \cdot {x}^{c} }$

We know that:

$\rm \longmapsto {x}^{a} \times {x}^{b} = {x}^{a + b}$

$\rm \longmapsto \dfrac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b}$

Therefore, we get:

$\rm = \dfrac{ {x}^{(a + b) + (b + c) + (c + a)}}{ {x}^{a + b + c} }$

$\rm = \dfrac{ {x}^{2(a + b+ c)}}{ {x}^{a + b + c} }$

$\rm = {x}^{2(a + b+ c) - (a + b + c)}$

$\rm = {x}^{a + b + c}$

7 0

2 years ago