#### Answer

a. {$x$|$x$ is a real number, $x\ne-6,\frac{7}{3}$}
b. $(-∞,-6)U(-6,\frac{7}{3})U(\frac{7}{3},∞)$

#### Work Step by Step

We are given the function $f(x)=\frac{2x+4}{3x^{2}+11x-42}$. The domain of the function will be all values of $x$ such that the denominator does not equal 0.
Therefore, we can set the denominator equal to 0. We will exclude from the domain all values of $x$ that make the denominator equal 0.
$3x^{2}+11x-42=0$
This factors into $(3x-7)(x+6)=0$.
Set both factors equal to 0.
$3x-7=0$, so $x=\frac{7}{3}$
$x+6=0$, so $x=-6$
Therefore, the domain is {$x$|$x$ is a real number, $x\ne-6,\frac{7}{3}$} in set-builder notation and $(-∞,-6)U(-6,\frac{7}{3})U(\frac{7}{3},∞)$ in interval notation.