Question

For what value of the constant c is the following function continuous at every number?

f(x)= { x+c if x<2
cx² +1 if x ≥ 2

Answer 1

The value of the constant c that makes the function continuous at every number is 1/3.

Step-by-step explanation:

In order for the function f(x) = { x+c if x<2, cx² +1 if x ≥ 2 to be continuous at every number, the two parts of the function must be equal when x = 2. This means that we need to find the value of c that makes x+c equal to cx² +1 when x = 2.

Substituting x = 2 into the function, we have 2+c = c(2)² +1. Simplifying this equation, we get 2+c = 4c+1. Rearranging, we have 3c = 1, so c = 1/3.

Therefore, for the function to be continuous at every number, the value of the constant c should be 1/3.