Mathematics

Problem

Let

f:\mathbb R\to \mathbb R

be given by

f(x)=x^{2}+p

, where

p\in\mathbb R

. Let

g:[0,\infty)\to\mathbb R

be defined by

g(t)=\sqrt{t}

. Determine all real values of

p

for which the composition

g\circ f

is defined for every

x\in\mathbb R