Let be defined by f(1)=a, ;f(2)=b, ;f(3)=c, ;f(4)=d

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

Problem

Let

f:\{1,2,3,4\}\to\{a,b,c,d\}

be defined by

f(1)=a,\;f(2)=b,\;f(3)=c,\;f(4)=d,

and let

g:\{a,b,c,d\}\to\{\alpha,\beta,\gamma,\delta\}

be defined by

g(a)=\beta,\;g(b)=\alpha,\;g(c)=\delta,\;g(d)=\gamma.

(i) Write down

f^{-1}

and

g^{-1}

. (ii) Compute

g\circ f

and then find

(g\circ f)^{-1}

. (iii) Evaluate

f^{-1}\circ g^{-1}

and compare it with your answer in part (ii). What conclusion do you draw?