Any function f(x) is an increasing function in [a, b] if :
(A) $\forall ~x_1, x_2 \in[a, b], f\left(x_1\right) ≥ f\left(x_2\right)$ if $x_1<x_2$
(B) $\forall ~x_1, x_2 \in[a, b], f\left(x_1\right) ≥ f\left(x_2\right)$ if $x_1>x_2$
(C) $\forall ~x_1, x_2 \in[a, b], f\left(x_1\right) ≤ f\left(x_2\right)$ if $x_1<x_2$
(D) $\forall ~x_1, x_2 \in[a, b], f\left(x_1\right) < f\left(x_2\right)$ if $x_1>x_2$
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 3
f(x) increasing in [a, b]
if for $\forall ~x_1, x_2 \in[a, b]$
$f(x_1) ≥ f(x_2)$ if $x_1 > x_2$
OR
$f(x_1) ≤ f(x_2)$ if $x_1 < x_2$
if value of y > x
then f(y) > x to be increasing in subsequent values