$g$ is monotonic strictly increasing, continuous in $ [0,\infty)$ and positive function.
10747
Given function $g$ continuous in line $[0,\infty)$...
17119
Find all strictly monotone $f:(0,+\infty) \to (0, +\infty)$ such that $f(\frac{x^2}{f(x)})=x.$
30940
Prove the integral of $f$ is positive if $f ≥ 0$, $f$ continuous at $x_0$ and $f(x_0)>0$
60700
Continuity of a function to the integers
13765
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
91852
A continuous, injective function $f: \mathbb{R} \to \mathbb{R}$ is either strictly increasing or strictly decreasing.
151427
f, g continuous for all rationals follow by continuous on all reals?
53349
Prove that $\sqrt{x}$ is continuous on its domain $[0, \infty).$
145368
How to show $f:Y\to X^{+}$ is continuous?
68048
Prove that if $f$ is differentiable on $[a,b]$ and $f'$ is monotonic on $[a,b]$ , $f'$ is continuous on $[a,b]$
28315
Monotone functions and non-vanishing of derivative
42567
Let $(a_n)_{n \geq 0}$ be a strictly decreasing sequence of positive real numbers , and let $z \in \mathbb C$ , $|z| < 1$.
50103
Show that a continuous function satisfying $f(2^x)=f(3^x)$ for $x\in (0,\infty)$ is a constant function
118353
For set of positive measure $E$, $\alpha \in (0, 1)$, there is interval $I$ such that $m(E \cap I) > \alpha \, m(I)$
73553
How is $a_n=(1+1/n)^n$ monotonically increasing and bounded by $3$?
46778
Prove that a recursive sequence is monotonically increasing
58816
Existence of a continuous function which does not achieve a maximum.