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

Evaluate The Function Found In The Previous Step At X2 class=

Sagot :

Given:

[tex]5x^2+2y=-3x-2y[/tex]

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

[tex]\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}[/tex]

We let y=f(x):

[tex]f(x)=\frac{-3x^{}-5x^2}{4}[/tex]

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

[tex]\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}[/tex]

Therefore,

[tex]f(-2)=-\frac{7}{2}[/tex]

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