Question

Let f(x)={cos(pi)(x), x is greater than or equal to -2
{x^2+k, x>2
find a value of k so that this function is continuous

Answer 1

replace \(x\) by \(-2\) in both expressions
set them equal, solve for \(k\)

Answer 2

You probably mean, x^2 + k, where x < 2.

If thats the case,

then lets see what happens at x = 2,

cos (2pi) = 1
x^2 + k = 4 + k,

so for f to be cont. at x = 2, 1 = 4+k

Hence, k = - 3.