The function defined by

has an inverse, and the inverse is defined for all real numbers. Find all possible values of k.

\(\text{We need to ensure that there is no discontinuity at $x=4$}\\ f(4) = 5\\ \lim \limits_{x\to 4^-} f(x) = 4+k\\ 5 = 4+k\\ k=1\)