Determine the value of ‘k’ for which the following function is continuous at x = 3: (All India 2017)

Let f (x) be defined by: f (x) = 2x /（3 + x） , x ≤ −2 k(x − 2), −2 < x < 4 2x − 6, x ≥ 4 Which of the following values of k would make f (x) continuous on R? a) k = 2 (b) k = 1 (c) There is no such value for k. (d) k = −1

Find the value for k so that the function will be continuous at x=4𝑥=4.f(x)=−8x2+64x−128x−4−73x2+24x+48+kifx<4ifx≥4

The table below shows certain values of k(x) on the interval [–17,–5].x k(x)–17 –11–13 –5–9 10–5 –14If k(x) is continuous on [–17,–5], can you conclude that the equation k(x)=–4 has a solution?

The function f is defined by f  x   = 3x + k, where k is a constant. Find the value of k if the graph of f passes through the point (−1, 8).

Determine the continuity of the function fx=x3-x