For the resistive circuit y(t)=bf(t), what condition ensures the system is time-invariant?

Correct option is B

​$$\text{A system is time-invariant if a time shift in the input results in the same time shift in the output, without changing the system behavior.} \\[8pt]\text{Given the system:} \\[6pt]y(t) = b f(t) \\[10pt]\bullet \ \text{If } b \text{ is constant, then shifting the input } f(t) \rightarrow f(t - t_0) \text{ gives:} \\[6pt]y(t) = b f(t - t_0) \\[8pt]\text{which is simply a shifted version of the original output } \Rightarrow \text{ time-invariant.} \\[10pt]\bullet \ \text{If } b \text{ were a function of time } b(t), \text{ the system response would change with time } \Rightarrow \text{ time-varying.}$$​​