Question

Evaluate the function found in the previous step at x=-2

Answer 1

Given:

`5x^2+2y=-3x-2y`

To evaluate the function at x=-2, we simplify the given relation first:

`\begin{gathered} 5x^2+2y=-3x-2y \\ \text{Simplify and rearrange} \\ 2y+2y=-3x-5x^2 \\ 4y=-3x^{}-5x^2 \\ y=\frac{-3x^{}-5x^2}{4} \end{gathered}`

We let y=f(x):

`f(x)=\frac{-3x^{}-5x^2}{4}`

Next, we plug in x=-2 into the function:

`\begin{gathered} f(x)=\frac{-3x^{}-5x^2}{4} \\ f(-2)=(-3(-2)-5(-2)^2)/(4) \\ \text{Simplify} \\ f(-2)=(-14)/(4) \\ f(-2)=-(7)/(2) \end{gathered}`

Therefore,

`f(-2)=-(7)/(2)`