If u(x) = -2x² + 3 and v(x) = 1/x what is the range of (u*v)(x)

Solution:

Given functions are

u(x) = -2x² + 3, v(x) = 1/x

The product of the two functions is :

u(x) * v(x) = (-2x² + 3) × (1/x)

(u*v)(x) = (-2x²)((1/x) + (3)(1/x)

=[-2x² /x]+ [3/x]

= -2x + 3/x

The range of the function (u*v)(x) is (∞, -∞)

If u(x) = -2x² + 3 and v(x) = 1/x what is the range of (u*v)(x)

Summary:

The range of (u*v)(x) is (∞, -∞)