is onetoone but not ontoSolutionSuppose fDR and gDR x0 is an

is one-to-one but not onto

Solution

Suppose f:DR and g:DR, x0 is an accumulation point of D, and f and g have limits at x0. If f(x)g(x) for all xD, then

limxx0f(x)limxx0g(x)

Assume that xD, f(x) and g(x) both have limits at some point x0 and f(x)g(x)

We know that limxx0f(x)=f(x0) and limxx0g(x)=g(x0)

f(x0)g(x0) because f(x)g(x) xD