Step 1: Identify functions requiring kernel interaction.
A system call is required when a function needs kernel services such as process control or scheduling.
Step 2: Analyze each option.
\texttt{exit} always invokes a system call to terminate the process.
\texttt{sleep} always invokes a system call to suspend execution.
\texttt{malloc} may allocate memory from user-space heap and does not always invoke a system call.
\texttt{strlen} is purely a user-space function and never invokes a system call.
Step 3: Conclusion.
Therefore, only \texttt{exit} and \texttt{sleep} always invoke system calls.