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

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

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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 \( x = \frac{9}{2} \).

Final Answer

The function \( f(x) \) is undefined at \( x = \frac{9}{2} \). Therefore, there is no numerical value for \( f\left(\frac{9}{2}\right) \).

\[ \boxed{\text{Undefined at } x = \frac{9}{2}} \]

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