# Simple Proof of Weierstass Approximation Theorem?

## Homework Statement

Let D={x in the set of real numbers: -3<x<3, x does not equal 0,1,2} and define g(x)=(cosx-1)/x + (x3-2x2-x+2)/(x2-3x+2) on D. Find G:R→R such that G is continuous everywhere and G(x)=g(x) when x is in set D.

## The Attempt at a Solution

From a past homework problem I know how to prove that, for any continuous f:R→R, there exists a sequence (pn) of polynomials such that pn converges uniformly to f on any given bounded subset of R.
So after I show that g(x) is continuous and that a sequence of polynomials that converges uniformly to g exists, how do I actually find the function G(x)?