Question

The following function is continuous at all points in the domain of real numbers. What is the value of n?
f(x)= 2x+2, if x > n
4x, if x $\leq$ n
A. -1
B. 0
C. 1/2
D.1

Answer 1

Answer:

D. 1

Step-by-step explanation:

To solve this problem, we just need to find the common point of these linear function, beacuse they form a piecewise function which is continuous according to the problem, that means they are related by one common point.

Let's solve the following expression $f(x)=g(x)$, where $f(x) =2x+2$ and $g(x)=4x$. So,

$2x+2=4x\\2=4x-2x\\2x=2\\x=1$

Which means $n=1$, that is, if the n is greater than 1, then the function is defined by $f(x)$, if the n is least or equal than 1, then the functioni is defined by $g(x)$

Therefore, the right answer is D.

Answer 2

Answer:

1. A, -1

2. D, 1

3. B, It is discontinuous because there is a value a for which f(a) is not defined 4. D, It is discontinuous because there is a value a such that lim f(x) does not exist