Respuesta :
ANSWER
[tex]Domain:(-\infty,\text{ 4\rparen U\lparen4, }\infty),\text{ \textbraceleft x \mid x}4\rbrace[/tex][tex]Range:\text{ \lparen-}\infty,\text{ 3\rparen U\lparen3, }\infty),\text{ \textbraceleft y \mid y}3\rbrace[/tex]EXPLANATION
Given:
[tex]f(x)\text{ = }\frac{1}{x\text{ - 4}}+\text{ 3}[/tex]Desired Outcome:
1. Domain
2. Range
Determine the domain of the function
Note: We want to include only input values that do not require the denominator to be 0 when there is a denominator. As a result, we'll set the numerator to 0 and solve for x.
[tex]\begin{gathered} 0\text{ = x - 4} \\ x\text{ = 4} \end{gathered}[/tex]We'll now remove 4 from the domain. All of the answers are real numbers x > 4 or x < 4. We will also use Union notation to combine the two sets.
That is:
[tex]Domain:(-\infty,\text{ 4\rparen U\lparen4, }\infty),\text{ \textbraceleft x \mid x}4\rbrace[/tex]
Determine the range of the function
Set x to 4 to find y
[tex]\begin{gathered} y\text{ = }\frac{1}{4-4}\text{ + 3} \\ y\text{ = 3} \end{gathered}[/tex]We'll also remove 3 from the range. All of the answers are real numbers y > 3 or y < 3. We will also use Union notation to combine the two sets.
That is:
[tex]Range:\text{ \lparen-}\infty,\text{ 3\rparen U\lparen3, }\infty),\text{ \textbraceleft y \mid y}3\rbrace[/tex]
