Integral Calculus> help help..........

help help.......

milind , 11 Years ago

Grade 12

1 Answers

Jitender Singh

Ans:

Hello Student,
Please find answer to the following question

$f(x, y ,z)\rightarrow (1, 2, 3)$
is a one-one function.
So which means that every input has only one output.
Given:
$f(x) = 1$
$f(y) \neq 1$
$f(z) \neq 2$
Since only one statement is correct and function is one-one.
Function has output 1 at x. So at y & z, it will have either 2 or 3. f(z) can be either 2 or 3. Since its not 2, so it will definitely be 3.
And f(y) be equal to 2. So we have
f(x) = 1
$f^{-1}(f(x)) = f^{-1}(1)$
Since function is one-one and also onto.
So it can be invertible. So,
$f^{-1}(f(x)) =x$
$f^{-1}(1) =x$
Option (a) is correct.

Last Activity: 11 Years ago