Question

Find k so that the following function is continuous on any interval: . . f(x)=kx if 0<=x<3 and f(x)=8x^2 if 3<=x. . K=?

Answer 1

To ensure continuity for the function at x = 3, the value of k must be 8 so that the function values from both piecewise segments match at that point.

Step-by-step explanation:

To find the value of k that makes the function f(x) continuous on any interval, we need to ensure the function values match at the point where the function definition changes, which is at x = 3. For the given function, f(x) = kx when 0 ≤ x < 3 and f(x) = 8x² when x ≥ 3, continuity at x = 3 means that k × 3 = 8 × 3². Solving this equation yields k = 8. Therefore, to ensure continuity at the point where x = 3, k must equal 8.

Answer 2

In finding the value of this inequality first is to substitute the X to the F(x) so that it would be rearrange to get the value of k. So if 3<=x, K is directly proportional to X so it means that K >=3