Let and Show that each one of f and g is one - one but (f + g) is not one - one.

Question

Philoid · Accepted Answer

Here in this range, the lines do not cut the curve in 2 equal valued points of y, therefore, the function f(x) = sinx is one - one.

in this range, the lines do not cut the curve in 2 equal valued points of y, therefore, the function f(x) = cosx is also one - one.

(f + g):[0,] →R = sinx + cosx

in this range the lines cut the curve in 2 equal valued points of y, therefore, the function f(x) = cosx + sinx is not one - one.

Hence,showed that each one of f and g is one - one but (f + g) is not one - one.