Questions: f(x)=(3x^2-6x+2)/(2x-9) x=9/2

Transcript text: $f(x)=\frac{3 x^{2}-6 x+2}{2 x-9} \quad x=\frac{9}{2}$

Solution

Solution Steps

To solve the problem, we need to evaluate the function $ f(x) = \frac{3x^2 - 6x + 2}{2x - 9} $ at $ x = \frac{9}{2} $. However, substituting $ x = \frac{9}{2} $ into the denominator $ 2x - 9 $ results in division by zero, which means the function is undefined at this point. Therefore, we cannot compute a numerical value for $ f(x) $ at $ x = \frac{9}{2} $.

Step 1: Define the Function

The function given is $ f(x) = \frac{3x^2 - 6x + 2}{2x - 9} $.

Step 2: Evaluate the Function at $ x = \frac{9}{2} $

To evaluate $ f(x) $ at $ x = \frac{9}{2} $, substitute $ x = \frac{9}{2} $ into the function: \[ f\left(\frac{9}{2}\right) = \frac{3\left(\frac{9}{2}\right)^2 - 6\left(\frac{9}{2}\right) + 2}{2\left(\frac{9}{2}\right) - 9} \]

Step 3: Check for Division by Zero

Calculate the denominator: \[ 2\left(\frac{9}{2}\right) - 9 = 9 - 9 = 0 \]

Since the denominator is zero, the function is undefined at $ x = \frac{9}{2} $.