Question

question 8
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let $f(x)=\

$$\begin{cases}2x - 4 & \\text{if } x \\leq 7\\\\-8x + b & \\text{if } x > 7\\end{cases}$$

$
if $f(x)$ is a function which is continuous everywhere, then we must have
b =
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Explanation:

Step1: Evaluate left-hand limit at $x=7$

$f(7) = 2(7) - 4 = 14 - 4 = 10$

Step2: Evaluate right-hand limit at $x=7$

$\lim_{x \to 7^+} f(x) = -8(7) + b = -56 + b$

Step3: Set limits equal for continuity

For continuity, $-56 + b = 10$

Step4: Solve for $b$

$b = 10 + 56 = 66$

Answer:

$66$