Question

question 6
let $f(x)=\

$$\begin{cases}8x - 3 & \\text{if } x \\leq 5 \\\\-5x + b & \\text{if } x > 5\\end{cases}$$

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

Explanation:

Step1: Find left limit at x=5

$\lim_{x \to 5^-} f(x) = 8(5) - 3$

Step2: Calculate left limit value

$\lim_{x \to 5^-} f(x) = 40 - 3 = 37$

Step3: Find right limit at x=5

$\lim_{x \to 5^+} f(x) = -5(5) + b$

Step4: Set limits equal for continuity

$37 = -25 + b$

Step5: Solve for b

$b = 37 + 25$

Answer:

$62$