Question

What is the period of the function f(x)=3sin(2x-1)+4

Answer 1

Coefficients, constant doesn't matter in period. only the "argument" or parameters or the angle matters.

if $f(x)$ has a period $T$ then $cf(ax+b)+d$ will have period of $\frac Ta$ (nothing matters other than that), $T$ is the fundamental period.

$\sin(x)$ has fundamental period is $2\pi$ so period of $fx)$ will be $\pi$