Explain the following properties of the functions.

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Explain the following properties of the functions. (1) Explain why

f(x)=x^2-4x+3

is a function but does not have an inverse function. (2) Explain why

g(x)=x^2-4x+3

x\geq2

, has the inverse function

g^{-1}(x)=2+\sqrt{1+x}

. (3) State the domain and range of

g

and

g^{-1}

. (4) Show that

(g\circ g^{-1})(x)=(g^{-1}\circ g)(x)=x

, the identity function.