Explanation:
To find the product of the two functions f(x) and g(x), denoted by f(x)•g(x), we need to multiply each term in f(x) by each term in g(x), and then simplify the result.
f(x) = 7x^3 - 5x^2 + 42x - 30
g(x) = 7x - 5
Multiplying each term in f(x) by each term in g(x), we get:
f(x)•g(x) = (7x^3)(7x) + (7x^3)(-5) + (-5x^2)(7x) + (-5x^2)(-5) + (42x)(7x) + (42x)(-5) + (-30)(7x) + (-30)(-5)
Simplifying each term, we get:
f(x)•g(x) = 49x^4 - 35x^3 - 35x^3 + 25x^2 + 294x - 210 - 210x + 150
Simplifying further, we get:
f(x)•g(x) = 49x^4 - 70x^3 + 25x^2 + 84x - 60
Therefore, the product of the two functions f(x) and g(x) is:
f(x)•g(x) = 49x^4 - 70x^3 + 25x^2 + 84x - 60