Question
The function \( f \) is defined as follows. \[ f(x)=\frac{x^{2}-9 x+8}{x^{2}-12 x+36} \] Find \( f(6) \). Simplify your answer as much as, possible. If applicable, click on "Undefined". \( f(6)= \) Undefined
Ask by Joseph Gray. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f(6) \) is undefined.
Solution
We are given the function
f(x) = (x² - 9x + 8) / (x² - 12x + 36).
To find f(6), substitute x = 6:
Numerator: 6² - 9·6 + 8 = 36 - 54 + 8 = -10.
Denominator: 6² - 12·6 + 36 = 36 - 72 + 36 = 0.
Since the denominator is 0, f(6) is undefined.
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Simplify this solution Extra Insights
Let's find \( f(6) \) first by substituting \( x = 6 \) into the function. \[ f(6) = \frac{6^{2} - 9 \times 6 + 8}{6^{2} - 12 \times 6 + 36} \] Calculating the numerator: \[ 6^{2} - 9 \times 6 + 8 = 36 - 54 + 8 = -10 \] Now, calculating the denominator: \[ 6^{2} - 12 \times 6 + 36 = 36 - 72 + 36 = 0 \] Having a denominator of 0 means \( f(6) \) is undefined. So, the final answer is: \( f(6) = \) Undefined
