Prove that the functions $h(x)=|f(x)|$ and $k(x)=\max\{f(x),g(x)\}$ are both continuous.
44574
Continuity of absolute value of a function
138105
Let $f$ and $g$ be continuous at $ x=a$, with $f(a)<g(a)$. Prove that there exists a neighborhood $I$ of a such that $f(x)<g(x)$ for all $x \in I$.
118207
Prove that the product of two continuous functions is continuous
154247
Proving $f(x)$ attains $\max$ or $\min$ when $f(x)\to0$ as $|x|\to\infty$.
98772
Continuity of a function in $\mathbb{R}$
129551
Does $\lim_{h\rightarrow 0}\ [f(x+h)-f(x-h)]=0$ imply that $f$ is continuous?
142494
Functions $f(x)/g(x), g(x)/h(x),h(x)/f(x)$ are constant
22061
$|f(x)-f(y)|\geq k|x-y|$.Then $f$ is bijective and its inverse is continuous.
71857
Proving that, $|f'(x)-f'(y)|\le k|x-y| \implies (f'(x))^2< 2 kf(x) $
60521
Continuity of a convex function
2142
Finding a set of continuous functions with a certain property 2
153798
Problem involving maximum and minimum of a continuous function
72044
prove $x \mapsto x^2$ is continuous
46629
Prove if $f(x) = g(x)$ for each rational number x and $f$ and $g$ are continuous, then $f = g$
34940
Continuity of $f(x) = x^n$
143174
property of continuous function
117502
Proving that a certain continuous function is surjective.