Question

Find the domain of the function ? what is the only value of x not in the domain answer in fraction form

Answer 1

Notice that f(x) is a rational function. In general, a rational function is defined for all values of the variable except for those that make the denominator equal to zero.

In our case,

$f(x)=\frac{1}{6x-2}$

Suppose that the denominator is equal to zero; then,

$\begin{gathered} 6x-2=0 \\ \Rightarrow6x=2 \\ \Rightarrow x=\frac{2}{6} \\ \Rightarrow x=\frac{1}{3} \end{gathered}$

Therefore, the only value of x not included in the domain of f(x) is x=1/3. The answer is 1/3.