19 f(x)=x^2-4 g(x)=2x+1 Solve fg(x)gt 0 Sho w c wor king.

To solve this inequality, first calculate fg(x) by multiplying function f(x) and g(x):fg(x)=f(x) * g(x)=(x^2 - 4)(2x+1)=2x^3+x^2-8x-4 > 0 Setting this equal to zero gives the roots of the equation2x^3 + x^2 - 8x - 4 = 0Since this equation is not easy to solve for by hand, we can determine the roots numerically and approximately find them to be: x ~ -2.101, -0.6438, and 1.7446To summarize:1. If x 02. If -2.101 04. If 1.7446 < x then 2x^3 + x^2 - 8x - 4 < 0This makes the solution to the given inequality as: x ∈ (-∞, -2.101) ∪ (-0.6438, 1.7446)