Question

A function f(x) is called as a strictly increasing function about a point ‘a’ If -

Where 'h' is a positive real number tending to zero.

• A. $f(a+h)>f\left(a\right)>f(a-h)$
• B. $f(a-h)>f\left(a\right)>f(a+h)$
• C. $f(a+h)\ge f\left(a\right)\ge f(a-h)$
• D. $f(a-h)\ge f\left(a\right)\ge f(a+h)$

Answer 1

The correct option is A

$f(a+h)>f\left(a\right)>f(a-h)$

If we are discussing the monotonicity of a function about a particular point we’ll consider only the neighborhood points.

And, from the general definition of strictly increasing function we know that if $x_1,x_2$ are two points in the domain of f(x) such that $x_2>x_1$ then $f\left(x_2\right)>f\left(x_1\right)$.

Here we know, a+h > a > a-h as ” h” is an infinitesimal positive number.

So, to be a strictly increasing function the condition should be f(a+h) > f(a) > f(a - h).