Uniform continuity of $x^\alpha$ on $[0,\infty)$

1. Define uniform continuity for a function f defined on a metric space X with distance function \(\rho ( x , y )\)

B Prove that if \(0 < \alpha < 1\) , then \(F ( x ) = x ^ { \alpha }\) is uniformly continuous on \([ 0 , \infty )\)