Answer
$(f \cdot g)(x) = 7x^3 + 5x^2$
$\text{Domain: all real numbers}$
Work Step by Step
This exercise asks us to multiply the two functions together. Let's write out the problem:
$(f \cdot g)(x) = f(x) \cdot g(x) = (7x + 5)(x^2)$
Distribute the terms:
$(f \cdot g)(x) = f(x) \cdot g(x) = (7x)(x^2) + (5)(x^2)$
Multiply to simplify:
$(f \cdot g)(x) = f(x) \cdot g(x) = 7x^3 + 5x^2$
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 $x$ so that we ca exclude them from the domain.
In this exercise, $x$ can be any real number, so the domain is all real numbers.
