Answer:
1. f(x) is continuous at x = 1
2. f(x) is continuous at x = 1
Step-by-step explanation:
Determine whether the function is continuous or discontinuous at x=1.
Examine the three conditions in the definition of continuity.
1. f(x) = x²+8 if x<1
2. f(x) = 6x² - 3 if x> 1
For a function to be continuous at a given x-value
then lim x→a f(x) = f(a)
Meaning that
What this is saying is that, as x gets closer to a , f(x) should also get closer to f(a).
1. Limit of f(x) = x² + 8 at x = 1
= 1²+8 = 9
f(a) = f(1) = 1² + 8 = 9.
lim x→a f(x) = f(a) = 9
2. Limit of f(x) = 6x² - 3 at x = 1
= 6(1²) - 3 = 3
f(a) = f(1) = 6(1²) - 3 = 3
lim x→a f(x) = f(a) = 3
