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Home » \( 4^3 = 64 \equiv 0 \) - Abu Waleed Tea

\( 4^3 = 64 \equiv 0 \) - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 t - 2 = 0 \Rightarrow t = 2

📌 Now check the numerator at $ t = 2 $:

📌 t^2 + 1 = 4 + 1 = 5

📌 Since the numerator is not zero when $ t = 2 $, and the denominator is zero, there is a vertical asymptote at $ t = 2 $. There are no common factors between numerator and denominator, so there are no holes.

📌 oxed{ ext{Vertical asymptote at } t = 2; ext{ no holes} }

📌 Question: A robotics engineer uses the function $ f(x) = \sqrt{x + 3} $ and $ g(x) = 2x - 1 $ to model sensor feedback and actuator response. What is the value of $ g(f(6)) $?

📌 Solution: First, evaluate $ f(6) $:

📌 f(6) = \sqrt{6 + 3} = \sqrt{9} = 3

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First, calculate the numerator:
\( 4(3)^2 = 4 imes 9 = 36 \)
\( 36 + 3 = 39 \)
Now calculate the denominator:
\( 3 - 1 = 2 \)

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