Question

given g(x), evaluate g(-2).
\\( g(x) = \frac{3x^2 - 2x}{2x} \\)
\\( g(-2) = ? \\)
simplify your answer.

Explanation:

Step1: Substitute x = -2 into g(x)

Substitute \( x = -2 \) into the function \( g(x)=\frac{3x^{2}-2x}{2x} \), we get \( g(-2)=\frac{3(-2)^{2}-2(-2)}{2(-2)} \).

Step2: Calculate the numerator

First, calculate the numerator: \( 3(-2)^{2}-2(-2)=3\times4 + 4 = 12 + 4 = 16 \).

Step3: Calculate the denominator

Then, calculate the denominator: \( 2(-2)=-4 \).

Step4: Divide numerator by denominator

Now, divide the numerator by the denominator: \( \frac{16}{-4}=-4 \).

Answer:

\( -4 \)