If $f,g$ are continuous at a , show that $h(x)=\max{f(x),g(x)}$ and $k(x)=min{f(x),g(x)}$, are also continuous at a (quick question)
57023
If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
5419
Continuous functions with $f^2(x)=g^2(x)\neq 0$
69122
If $f,g$ are uniformly continuous prove $f+g$ is uniformly continuous but $fg$ and $\dfrac{f}{g}$ are not
46834
show that a distance function is continuous
20273
Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.
53627
Proving continuity of $f$
64619
Continuity of a function of product spaces
151410
Inequality of continuous functions
105652
Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$
154881
Question on differentiability of a continuous function
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
149095
$f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
62270
Given two increasing continuous functions $f,g$ prove that $(b-a) \int^b_a f(x)g(x) dx > \int^b_a f(x) dx \int^b_a g(x) dx$
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
44269
If $f$ is nonnegative and continuous on $[a,b]$, then $\left(\int_a^b f(x)^n \ dx\right)^{1/n}\to\max\limits_{[a,b]} f$
155923
continuity of $f(x,y)$ in $\mathbb R^2$.