Let the function f: R → R be defined


 Let the function f: R → R be defined by f (x) = cos x, ∀ x ∈ R. Show that f is neither one-one nor onto.


We have,

f: R → R, f(x) = cos x


f (x1) = f (x2)

cos x1 = cos x2

x1 = 2nπ ± x2, n ∈ Z

It’s seen that the above equation has infinite solutions for x1 and x2

Hence, f(x) is many one function.

Also the range of cos x is [-1, 1], which is subset of given co-domain R.

Therefore, the given function is not onto.

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now