Question

If u(x) = −2x² +3 and v(x)=1/x, what is the range of (uv)(x)?

Answer 1

Given:

`\begin{gathered} u(x)=-2x^2+3 \\ v(x)=(1)/(x) \end{gathered}`

Required:

To find the range of the function (uv)(x).

Step-by-step explanation:

We know that

`\begin{gathered} (uv)(x)=u(v(x)) \\ \\ =u((1)/(x)) \\ \\ =-2((1)/(x^2))+3 \\ \\ =-(2)/(x^2)+3 \end{gathered}`

The horizontal asymptote of this function is at y=3.

So, the range of this function is from

`(-\infty,3)`

Final Answer:

The range of (uv)(x) is

`(-\infty,3)`