Question

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

Answer 1

`(-\infty,-(4)/(3))\cup(-(4)/(3),\infty)`

Explanation:

Given f(x) defined below:

`f\mleft(x\mright)=(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=-(4)/(3) \end{gathered}`

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

Therefore, the domain of f(x) is:

`(-\infty,-(4)/(3))\cup(-(4)/(3),\infty)`