Question

Given f(x)=x+3 if x≠3 and f(x)=2+ √ k if x=3, find k if f(x) is continuous.

Answer 1

To find the value of k if f(x) is continuous, we need to ensure that the two parts of the piecewise function, f(x) = x + 3 and f(x) = 2 + √k, are equal at x = 3. Setting the two parts equal to each other and solving for k gives k = 16.

Step-by-step explanation:

To find the value of k if f(x) is continuous, we need to ensure that the two parts of the piecewise function, f(x) = x + 3 and f(x) = 2 + √k, are equal at x = 3.

Using the first part of the function, x + 3, we have f(3) = 3 + 3 = 6.

Setting this equal to the second part of the function, 2 + √k, we get 6 = 2 + √k. Solving for k, we subtract 2 from both sides and then square both sides to get k = 16.