Question

True or False? Picture provided below

Answer 1

Answer:

The statement is true

Step-by-step explanation:

To answer this question we must take the limit of f(x) when the function tends to 1. We must take this limit by the right and the left of 0. $(-1 ^{+}; -1 ^{-})$. If any of these limits tends to infinity then the function is discontinuous at x = -1.

But if the

$\lim_{x \to \\-1^+}f(x)=\lim_{x \to \\-1^-}f(x) = b$      Where b is a real number

Then the function is continuous at x = -1

Then.

$\lim_{x \to \\-1^+}f(x) = \lim_{x \to \\-1^+}-2x +1\\\\\lim_{x \to \\-1^+}-2(-1) +1 = 3$

and

$\lim_{x \to \\-1^-}f(x) = \lim_{x \to \\-1^-} 2x+5\\\\\lim_{x \to \\-1^-} 2(-1)+5 = 3$

Then:

$\lim_{x \to \\-1^+}f(x) = \lim_{x \to \\-1^-}f(x) = 3$

Therefore the function is continuous at x = -1. The statement is true