Question

Domain of f(x)=2/(3x+4)

Answer 1

Answer:

$(-\infty,-\frac{4}{3})\cup(-\frac{4}{3},\infty)$

Explanation:

Given f(x) defined below:

$f\mleft(x\mright)=\frac{2}{3x+4}$

The domain of f(x) is the set of the values of x for which f(x) is defined.

Find the excluded values, the values at which f(x) is undefined. To do this, set the denominator equal to 0 and solve for x.

$\begin{gathered} 3x+4=0 \\ 3x=-4 \\ x=-\frac{4}{3} \end{gathered}$

The excluded value of the domain is -4/3.

Therefore, the domain of f(x) is:

$(-\infty,-\frac{4}{3})\cup(-\frac{4}{3},\infty)$