Question

Explain why a function must be one-to-one in order to have an inverse. Use graphical or algebraic support. Write in complete sentences.

Answer 1

because if \(f\) is not injective, then the inverse relation \(f^{-1}\) will not be a function.

Answer 2

for instance, let \(f:\{a,b,c\}\to\{1,2,3\}\) given by
\[ \large f=\{(a,1),(b,2),(c,1)\} \]
whose inverse relation is
\[ \large f^{-1}=\{(1,a),(2,b),(1,c)\}. \]
This last relation is not a function on two accounts: (1) 3 does not map to any element of \(\{a,b,c\}\), and (2) 1 maps to two elements a and c.

Answer 3

THANK YOU!!

Answer 4

u r welcome