Question

Give the intervals where g(x)=(3x)/(x+2)is continuous

Answer 1

The function g(x) = (3x)/(x+2) is continuous for all values of x except x = -2. The intervals where g(x) is continuous are (-∞,-2) and (-2,∞).

Step-by-step explanation:

A function is continuous if there are no breaks, holes, or jumps in the graph. To determine where the function g(x) = (3x)/(x+2) is continuous, we need to find the intervals where the denominator (x+2) is not equal to zero. Since the function is undefined when the denominator is zero, we can find the intervals by setting the denominator equal to zero and solving for x:

(x+2) = 0

x = -2

So, the function is continuous for all values of x except x = -2. Therefore, the intervals where g(x) is continuous are (-∞,-2) and (-2,∞).