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
`(\pi)/(b)`.

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