Let be any bijective function with inverse

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

f

be any bijective function with inverse

f^{-1}

. (i) Explain why

f\bigl(f^{-1}(x)\bigr)=x

for every

x

in the domain of

f^{-1}

. (ii) Using logical reasoning based on part (i), simplify the expression

f^{-1}\bigl(f\bigl(f^{-1}\bigl(f(x)\bigr)\bigr)\bigr)

, justifying each step of your argument. (iii) Write two different nested compositions involving only

f

and

f^{-1}

that are identically equal to

x

, and briefly state the reason for their equality.