Question

What is the largest interval containing zero on which f(x)=sinx is one-to-one?

Answer 1

Answer:  The answer is $[0,\pi).$

Step-by-step explanation:  We are given to find the largest interval containing zero on which the function f(x) = sin x is one-to-one.

Attached herewith the graph of f(x) = sin x. We know that the domain is           (-∞, +∞) and the range is (-1, 1).

We can see that $f(0)=f(\pi)=f(2\pi)=0.$. The interval in which f(x) is one-to one is $[0,2\pi]$, except at the points $0,~\pi,~2\pi$. Since we need to include zero in the interval, so the largest possible interval will be

$I=[0,\pi)$

Thus, the answer is  $I=[0,\pi)$.