Answer:
[tex]x=\frac{34}{7}[/tex]
Explanations:
Given the function defined as:
[tex]\begin{gathered} f(x)=-7+\frac{-8}{x-6} \\ \end{gathered}[/tex]
The function can further be expressed as:
[tex]f(x)=-7-\frac{8}{x-6}[/tex]
Find the LCM of the function;
[tex]\begin{gathered} f(x)=\frac{-7(x-6)-8}{x-6} \\ f(x)=\frac{-7x+42-8}{x-6} \\ f(x)=\frac{-7x+34}{x-6} \\ \end{gathered}[/tex]
If f(x) = 0, then the value of x is calculated as:
[tex]\begin{gathered} \frac{-7x+34}{x-6}=0 \\ -7x+34=0 \\ -7x=0-34 \\ -7x=-34 \end{gathered}[/tex]
Divide both sides of the equation by -7:
[tex]\begin{gathered} \frac{\cancel{-7}x}{\cancel{-7}}=\frac{\cancel{-}34}{\cancel{\square}7} \\ x=\frac{34}{7} \end{gathered}[/tex]
Therefore the value of x if f(x) = 0 is 34/7
