Question

Which among the following won't represent a function ?

• A. $f:R\to N,f\left(x\right)=x$
• B. $f:[0,\infty )\to [0,\infty ),f\left(x\right)=x^2-1$
• C. $f:N\to R,f\left(x\right)=x^{2/3}+1$
• D. $f:R\to R,f\left(x\right)=x|x|$

Answer 1

Answer: (A), (B)

The correct options are
A $f:R\to N,f\left(x\right)=x$
B $f:[0,\infty )\to [0,\infty ),f\left(x\right)=x^2-1$

$f:R\to N,f\left(x\right)=x$
$f\left(0\right)=0\notin N$
$\therefore$ Not a function

$f:[0,\infty )\to [0,\infty ),f\left(x\right)=x^2-1$
$f\left(0\right)=0-1=-1\notin [0,\infty )$
$\therefore$ Not a function

For the other two options, each element in the domain has a unique image in the codomain, therefore, are functions.