Mathematics

Mathematics

Problem

Let

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

be defined by

f(x)=x^{2}

and

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

be defined by

g(t)=\sqrt{k-t}

, where

k

is a real parameter. For which value(s) of

k

is the composition

g\circ f

defined for every real

x

? a)

k>0

b)

k\ge 0

c) No real value of

k

d)

k\ge 1

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