Question - Determining the Domain of a Function
Solution:
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 $$-\frac{7}{6}$$.
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