Question
Given \( f(x) \), evaluate \( f(6) \), \( f(x)=\frac{x^{2}-x}{2 x+3} \) \( f(6)=[?] \) Simplify your answer.
Ask by Howell Vega. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f(6) = 2 \)
Solution
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The Deep Dive
To evaluate \( f(6) \) given the function \( f(x) = \frac{x^{2} - x}{2x + 3} \), we substitute \( x \) with 6: \[ f(6) = \frac{6^{2} - 6}{2(6) + 3} \] Calculating the numerator: \[ 6^{2} - 6 = 36 - 6 = 30 \] Calculating the denominator: \[ 2(6) + 3 = 12 + 3 = 15 \] Now, substituting these values back into the function: \[ f(6) = \frac{30}{15} = 2 \] Thus, \( f(6) = 2 \).
