Question

List all real values of x such that f(x) = 0, if there are no such real x, type DNE in the answer blank. If there is more than one real x, give a comma separated list (i.e: 1, 2) X =

Answer 1

`x=(34)/(7)`

Explanations:

Given the function defined as:

`\begin{gathered} f(x)=-7+(-8)/(x-6) \\ \end{gathered}`

The function can further be expressed as:

`f(x)=-7-(8)/(x-6)`

Find the LCM of the function;

`\begin{gathered} f(x)=(-7(x-6)-8)/(x-6) \\ f(x)=(-7x+42-8)/(x-6) \\ f(x)=(-7x+34)/(x-6) \\ \end{gathered}`

If f(x) = 0, then the value of x is calculated as:

`\begin{gathered} (-7x+34)/(x-6)=0 \\ -7x+34=0 \\ -7x=0-34 \\ -7x=-34 \end{gathered}`

Divide both sides of the equation by -7:

`\begin{gathered} \frac{\cancel{-7}x}{\cancel{-7}}=\frac{\cancel{-}34}{\cancel{\square}7} \\ x=(34)/(7) \end{gathered}`

Therefore the value of x if f(x) = 0 is 34/7