Question

6/(x) = X". Whi
Define many one mapping. I
f(x) = x2 is a many one mappi​

Answer 1

Correct question :- Define many one mapping. Is f(x) = x² is a many one mapping ?

Solution :-

Many-one mapping

If a function y = f(x) gives the same value(y) for two different x , say $x_1\:and\:x_2$ ,then the function is called many one mapping.

Methods to check if a function is many-one.

Put $x_1\:and\:x_2$ in the given function and equate them.If we get one more solution other than $x_1\:=\:x_2$ ,then function is many-one.

In the given question ,we have y = x².

Checking :- put $x\:=x_1\:and\:x_2$

=> ${x_1}^2\:=\:{x_2}^2$

=> ${x_1}^2\:-\:{x_2}^2\:=0$

=> $(x_1\:-\:x_2\:)\: \: (x_1\:+\:x_2\:)\:=0$

=> $x_1\:=\:x_2\:or\: x_1\:=\:-\:x_2\:\:$

Hence,we get another solution other than $x_1\:=\:x_2$ . Hence,it is a many-one function.