Question

If $I$ be an open interval contained in the domain of a real valued function $f$ and if $x_1<x_2$ in $I$, then which of the following statements is true?

• A. $f$ is said to be decreasing on $I$, if $f\left(x_1\right)>f\left(x_2\right)$ for all $x_1,x_2\in I$
• B. $f$ is said to be strictly decreasing on $I$, if $f\left(x_1\right)\ge f\left(x_2\right)$ for all $x_1,x_2\in I$
• C. Both(a) and (b) are true
• D. Both(a) and (b) are false

Answer 1

Answer: (D)

If $I$ be an open interval contained in the domain of a real valued function $f$, then $f$ is said to be

(a) Decreasing on I, if $x_1<x_2$ in $I$
$\Rightarrow f\left(x_1\right)\ge f\left(x_2\right)$ for all $x_1,x_2\in I$.
(b) Strictly decreasing on $I$, if $x_1<x_2$ in $I$
$\Rightarrow f\left(x_1\right)>f\left(x_2\right)$ for all $x_1,x_2\in I$.
Note Figure given below, shows that function is neither increasing nor decreasing.