Question

f(x)= {3x+2, x greater than or equal to 1 and 2k-x, x<1. (find the value of the constant k that will make the function continuos)

Answer 1

f(x) will be a continuous function if\[\lim_{x \rightarrow 1}f(x)=\lim_{x \rightarrow 1+}f(x)=\lim_{x \rightarrow 1-}f(x)=f(1)\]

Answer 2

\[\lim_{x \rightarrow 1+}3x+2=3\times1+2=5\]\[\lim_{x \rightarrow 1-}2k-x=2k-1\]In order for the function to be continuous\[2k-1=5\]\[2k=6\]\[k=3\]