Answer: (fg)(x) = 3x^2 - 3
Explanation:
To find (fg)(x), we need to substitute the function g(x) into the function f(x) and simplify the expression. Given:f(x) = 3xg(x) = x^2 - 1 To find (fg)(x), we substitute g(x) into f(x):(fg)(x) = f(g(x))Substituting g(x) = x^2 - 1 into f(x):(fg)(x) = f(g(x)) = f(x^2 - 1)Now, we substitute f(x) = 3x into the expression f(x^2 - 1):(fg)(x) = 3(x^2 - 1)Expanding the expression:(fg)(x) = 3x^2 - 3So, the function (fg)(x) is 3x^2 - 3.Now, let's determine the domain of the function (fg)(x). The domain represents all the possible values that x can take in the function. Since there are no restrictions on x in the given functions f(x) = 3x and g(x) = x^2 - 1, we can conclude that the domain of (fg)(x) is all real numbers .Therefore, the function (fg)(x) = 3x^2 - 3 and its domain is all real numbers