How do you find the domain for #f(x)=1/(3x+2)#?

To find the domain of the function ( f(x) = \frac{1}{3x + 2} ), we need to identify any values of ( x ) that would make the denominator zero, as division by zero is undefined. Therefore, we set the denominator, ( 3x + 2 ), not equal to zero and solve for ( x ).

[ 3x + 2 \neq 0 ] [ 3x \neq -2 ] [ x \neq -\frac{2}{3} ]

So, the domain of the function is all real numbers except ( x = -\frac{2}{3} ). Therefore, the domain is ( (-\infty, -\frac{2}{3}) \cup (-\frac{2}{3}, \infty) ).

To find the domain of ( f(x) = \frac{1}{3x + 2} ), identify any values of ( x ) that would result in division by zero. In this case, the denominator ( 3x + 2 ) cannot equal zero, so solve the equation ( 3x + 2 = 0 ) to find the value(s) of ( x ) that make the denominator zero. Once you find the solution(s) for ( x ), exclude them from the domain. Thus, the domain of ( f(x) ) is all real numbers except the value that makes the denominator zero.