question_answer

Which one of the following functions is one-to-one?

A)  \[f(x)=\sin x,x\in [-\pi ,\pi ]\]

B)  \[f(x)=\sin x,x\in \left[ -\frac{3\pi }{2},-\frac{\pi }{4} \right]\]

C)  \[f(x)=\cos x,x\in \left[ -\frac{\pi }{2},\frac{\pi }{2} \right]\]

D) \[f(x)=\cos x,x\in [\pi ,2\pi )\]

E)  \[f(x)=\cos x,x\in \left[ -\frac{\pi }{4},\frac{\pi }{4} \right]\]

Correct Answer: D

Solution :

In the given options (a), (b), (c), (e) the curves are decreasing and increasing in the given intervals, so it is not one-to-one function. But in option (d), the curve is only increasing in the given intervals, so it is one-to-one function.