If the function is <strong>CONTINUOUS</strong>, then what is the value of k?
For the following two (02) items: Consider the function f(x)=\begin{cases}4(5^{x}),&x \lt 0\\ 8k+x,&x \geq 0\end{cases}
- A. 0.5 ✓
- B. 1
- C. 1.5
- D. 2
Correct Answer: A. 0.5
Explanation
For f(x) to be continuous at x=0, the left-hand limit must equal the right-hand limit and f(0). The left-hand limit is \lim_{x \to 0^-} 4(5^x) = 4(1) = 4. The value at x=0 is 8k+0 = 8k. Equating them gives 8k = 4, which implies k = 0.5.
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