The function defined by
\[f(x) = \left\{
\begin{array}{cl}
x + k & \text{if $x < 4$}, \\
2x - 3 & \text{if $x \ge 4$}
\end{array}
\right.\]has an inverse, and the inverse is defined for all real numbers.  Enter all possible values of $k,$ separated by commas.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The function defined by
\[f(x) = \left\{
\begin{array}{cl}
x + k & \text{if $x < 4$}, \\
2x - 3 & \text{if $x \ge 4$}
\end{array}
\right.\]has an inverse, and the inverse is defined for all real numbers.  Enter all possible values of $k,$ separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1
The function defined by
\[f(x) = \left\{
\begin{array}{cl}
x + k & \text{if $x < 4$}, \\
2x - 3 & \text{if $x \ge 4$}
\end{array}
\right.\]has an inverse, and the inverse is defined for all real numbers.  Enter all possible values of $k,$ separated by commas.
train