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:

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

Therefore,

$f(-2)=-\frac{7}{2}$