Determining the Domain of a Function
The function provided is:
\[ f(x) = \frac{1}{6x + 7} \]
To find the domain of this function, we must determine the values of x for which the function is defined. Since we have a fraction with a denominator of \(6x + 7\), we must ensure that the denominator is never 0, because division by zero is undefined.
So we set up the inequality:
\[ 6x + 7 \neq 0 \]
Solving for x, we subtract 7 from both sides:
\[ 6x \neq -7 \]
And then divide by 6:
\[ x \neq \frac{-7}{6} \]
Thus, the only value that x cannot take (the only value not in the domain) is \(-\frac{7}{6}\).
