Question

Let $f$ be an injective function with domain $\{x,y,z\}$ and range $\{1,2,3\}$ such that exactly one of the following statements is correct and the remaining are false $f\left(x\right)=1,f\left(y\right)\ne 1,f\left(z\right)\ne$ 2. The value of $f^{-1}\left(1\right)$ is:

• A. $x$
• B. $y$
• C. $z$
• D. None

Answer 1

Answer: (B)

$y$

Let us assume the 3rd statement is correct. As f is injective then $f\left(y\right)=1$ or $f^{-1}\left(1\right)=y$

Assuming 1st statement to be correct necessarily makes 2nd true while assuming the 2nd to be true doesn't give any necessary conclusion so our assumption is the only one possible.