Mathematics

Mathematics

Problem

Let

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

be defined by

f(x)=x^{2}

and let

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

be defined by

g(x)=\sqrt{x}

(principal square root). Which statement is correct? a) Both

f\bigl(g(x)\bigr)=x

for all

x\ge 0

and

g\bigl(f(x)\bigr)=x

for all

x\in\mathbb R

b)

g\bigl(f(x)\bigr)=x

for every

x\in\mathbb R

, but

f\bigl(g(x)\bigr)\neq x

for some

x\ge 0

c)

f\bigl(g(x)\bigr)=x

for every

x\ge 0

, but

g\bigl(f(x)\bigr)\neq x

for some

x\in\mathbb R

d) Neither composition equals

x

for all admissible

x

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