Answer the following questions related to inverse functions.

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

Problem

Answer the following questions related to inverse functions. (i) State the relationship between the domain and range of a function

f

and those of its inverse

f^{-1}

, provided

f

is bijective. (ii) Prove the relationship stated in (i) directly from the definition of an inverse function. (iii) A bijective function

f

has domain

(0,5]

and range

[-3,4)

. Determine the domain and the range of

f^{-1}

. Justify your answer clearly.