Question

Which of the following is NOT a function?

• A. $f:N\to N$ defined by $f\left(x\right)=2x+5$
• B. $f:(-\infty ,0]\to [0,\infty )$ defined by $f\left(x\right)=\sqrt{-x}$
• C. $f:Z\to N$ defined by $f\left(x\right)=x-100$
• D. $f:N\to R$ defined by $f\left(x\right)=\frac{2x-5}{3}$

Answer 1

The correct option is C $f:Z\to N$ defined by $f\left(x\right)=x-100$

$f:N\to N,f\left(x\right)=2x+5$
$f$ is defined for all $x\in N$.
So, Range $=\{7,9,11,\dots \}\subset N$
$\therefore f$ is a function.

$f:(-\infty ,0]\to [0,\infty ),f\left(x\right)=\sqrt{-x}$
$f$ is defined if $-x\ge 0$
$\Rightarrow x\le 0\Rightarrow x\in (-\infty ,0]$.
So, Range $=[0,\infty )$
$\therefore f$ is a function.

$f:Z\to N,f\left(x\right)=x-100$
$f\left(0\right)=-100\notin N$
$\therefore f$ is not a function.

$f:N\to R,f\left(x\right)=\frac{2x-5}{3}$
$f$ is defined $\forall x\in N$.
So, Range $=\{-1,\frac{-1}{3},\frac{1}{3},1,\dots \}\subset R$
$\therefore f$ is a function.