solution:
we are consider the following function,
f(x)=3x+k,x\leq 3
=kx^{2}-6,x>3
\lim_{x\rightarrow 3^-}(3x+k)=9+k
\lim_{x\rightarrow3^+}
(kx^{2}-6)=9k-6
so the left and right limits are equal.
therefore, the function is continuous at x=3
so,the therom of the function is continous at x=3
9k-6=9+k
8k=15
k=15/8
=1.875
therefore,the value of k=1.875
