If $f$ is a non$-$constant entire function, prove that the range $f(C)$ of $f$ must almost "fill up$"$ the

complex plane in the following precise sense: for every point $w_0$inC and every $r>0$ the range

of $f$ has non$-$empty intersection with the disk $(w_0,r).($N$.$B$.$ The technical description of this

situation is that $f(C)$ is dense in $C.$ Hint: Under the assumption that the assertion were false

for some $w_0$ and $r,$ derive a contradiction by considering the function $g(z)=[f(z)-w_0{]}^{-1}.)$