Answer
$3f(x) - 2 = 6x + 13$
$\text{The domain is the set of all real numbers.}$
Work Step by Step
This exercise asks us to subtract $2$ from three times $f(x)$. Let's write out the problem:
$3f(x) - 2 = 3(2x + 5) - 2$
Distribute terms first to get rid of the parentheses:
$3f(x) - 2 = 6x + 15 - 2$
Combine like terms:
$3f(x) - 2 = 6x + 13$
When we find the domain, we want to find which values of $x$ will cause the function to become undefined; in other words, we want to find any restrictions for $x$. In this exercise, $x$ can be any real number since there are no restrictions, so the domain is all real numbers.
