The function is defined by and by

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

The function

f:[2,\infty)\to[0,\infty)

is defined by

f(x)=\sqrt{x-2}

and

g:[0,\infty)\to[2,\infty)

g(x)=x^{2}+2

. Which of the following describes the relationship between

f

and

g

? (a)

f\circ g=I_{[0,\infty)}

but

g\circ f\neq I_{[2,\infty)}

, so they are not mutual inverses (b)

g\circ f=I_{[2,\infty)}

but

f\circ g\neq I_{[0,\infty)}

, so they are not mutual inverses (c)

f\circ g=I_{[0,\infty)}

and

g\circ f=I_{[2,\infty)}

, so they are mutual inverses (d) Neither composition equals the identity on its domain