Question

If f(x) is discontinuous, determine the reason.
`f(x) = \left \{ {{x^2 + 4; x \leq 1} \atop {x+4; x \ \textgreater \ 1}} \right.`a. f(x) is continuous for all real numbersb. The limit as x approaches 1 does not exist c. f(1) does not equal the limit as x approaches 1 d. f(1) is not defined

Answer 1

a. f(x) is continuous for all real numbers

Explanation:

At x = 1

Piece 1:

f(x) = 1² + 4 = 5

Piece 2:

f(x) = 1 + 4 = 5

First piece ends at (1,5)

Second piece starts at (1,5)

So no discontinuity