To determine the domain of the function [tex]\( f(x) = \frac{1}{7x + 5} \)[/tex], we need to identify all possible values of [tex]\( x \)[/tex] for which the function is defined. The function will be undefined whenever the denominator is equal to zero, because division by zero is undefined.
Let's find when the denominator [tex]\( 7x + 5 \)[/tex] equals zero:
[tex]\[
7x + 5 = 0
\][/tex]
Solve for [tex]\( x \)[/tex] by isolating [tex]\( x \)[/tex]:
[tex]\[
7x = -5
\][/tex]
[tex]\[
x = \frac{-5}{7}
\][/tex]
The function [tex]\( f(x) = \frac{1}{7x + 5} \)[/tex] is undefined at [tex]\( x = \frac{-5}{7} \)[/tex].
Therefore, the only value of [tex]\( x \)[/tex] that is not in the domain is:
[tex]\[
\boxed{-\frac{5}{7}}
\][/tex]
