Question

Let $X=\{-1$, $0$, $1\}$, $Y=\{0$, $2\}$ and a function $f:X\to Y$ defined by $y=2x^4$, is

• A. one-one onto
• B. one-one into
• C. many-one onto
• D. many-one into

Answer 1

Answer: (C)

We have, $y=2x^4$
$\therefore y(-1)=y(1)=2$, $y(0)=0$ (many-one onto)
Here, we see that for two different values of $x$, we will get a same image and no element of $y$ is left, which do not have pre-image. So, function is many-one onto.