Question

ifA=(3, 01,7) and f:AtoB is an on to function defined by f(x) =3x-5 then B is​

Answer 1

$\textbf{Given:}$

$A=\{3,0,1,7\}\;\text{and}$

$\text{f(x)=3x-5 is an onto function}$

$\textbf{To find:}$

$\text{B}$

$\textbf{Solution:}$

$\textbf{Onto:}$

$\text{A function f:A\implies\,B is said to be onto if}$

$\textbf{Range of f = Co-dmain}$

$\text{First we find images of each element of A}$

$f(3)=3(3)-5=9-5=4$

$f(0)=3(0)-5=0-5=-5$

$f(1)=3(1)-5=3-5=-2$

$f(7)=3(7)-5=21-5=16$

$\text{Since f is onto, we have}$

$\text{Co-domain = Range of f}$

$\implies\bf\,B=\{-5,-2,4,16\}$