Let $S=\{a, b, c\}$ and $T=\{1,2,3\} .$ Find $F^{-1}$ of the following functions $F$ from $S$ to $T$. if it exists.  $F =\{( a , 3),\,( b , 2),\,( c , 1)\}$

Vedclass pdf generator app on play store
Vedclass iOS app on app store

$S =\{ a , b , c \}, \,\,T =\{1,2,3\}$

$F : S \rightarrow T$ is defined as $F =\{( a , 3),\,( b , 2),\,( c , 1)\}$

$\Rightarrow $ $F ( a )=3, \,F ( b )=2,\, F ( c )=1$

Therefore, $F^{ -1}: T \rightarrow $ $S$ is given by $  F ^{-1}=\{(3, a ),\,(2, b ),\,(1, c )\}$

Similar Questions

State with reason whether following functions have inverse $h:\{2,3,4,5\} \rightarrow\{7,9,11,13\}$ with $h=\{(2,7),(3,9),(4,11),(5,13)\}$

Consider $f:\{1,2,3\} \rightarrow\{a, b, c\}$ and $g:\{a, b, c\} \rightarrow$ $\{$ apple, ball, cat $\}$ defined as $f(1)=a$, $f(2)=b$,  $f(3)=c$,  $g(a)=$ apple, $g(b)=$ ball and $g(c)=$ cat. Show that $f,\, g$ and $gof$ are invertible. Find out $f^{-1}, \,g^{-1}$ and $(gof)^{-1}$ and show that $(gof)^{-1}=f^{-1}og^{-1}$

Consider $f: R _{+} \rightarrow[-5, \infty)$ given by $f(x)=9 x^{2}+6 x-5 .$ Show that $f$ is invertible with $f^{-1}(y)=\left(\frac{(\sqrt{y+6})-1}{3}\right)$

Let f : $R \to R$ be defined by $f\left( x \right) = \ln \left( {x + \sqrt {{x^2} + 1} } \right)$ , then number of solutions of $\left| {{f^{ - 1}}\left( x \right)} \right| = {e^{ - \left| x \right|}}$ is

If $f(x) = {x^2} + 1$, then ${f^{ - 1}}(17)$ and ${f^{ - 1}}( - 3)$ will be