Question

The function below models the voltage, in volts, of a certain alternating current after x seconds, where A and b are positive constants.
f(x) = Acos(bx)
Assume the expression inside the cosine function is measured in radians.
What is the largest value of c such that when the voltage's domain is restricted to the interval [0,c], the function is invertible

Answer 1

First of all, we can just ignore A, it has no effect but to vertically stretch our cosine.

If it was only $f(x)=cosx$, the function would be invertible as long as it's confined between $0$ and $\pi$. Now, the argument of our cosine is not $x$ but $bx$. It means that it won't stop at $\pi$, but at $\frac{\pi}{b}$.

Another way to think about it, "what should i replace x with so I get $\pi$ inside the cosine?"