Answer
a. {$x$|$x$ is a real number, $x\ne-\frac{7}{2}$}
b. $(-∞,-\frac{7}{2})U(-\frac{7}{2},∞)$
Work Step by Step
We are given the function $f(x)=\frac{8x-3}{2x+7}$. 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.
$2x+7=0$
Subtract 7 from both sides.
$2x=-7$
Divide both sides by 2.
$x=-\frac{7}{2}$
Therefore, the domain is {$x$|$x$ is a real number, $x\ne-\frac{7}{2}$} in set-builder notation and $(-∞,-\frac{7}{2})U(-\frac{7}{2},∞)$ in interval notation.