If $f: \mathbb R^2 \rightarrow \mathbb R$ is a continuous function such that $f(x)=0$ for only finitely many values of $x$,
101319
Properties of a continuous map $f : \mathbb{R}^2\rightarrow \mathbb{R}$ with only finitely many zeroes
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
155923
continuity of $f(x,y)$ in $\mathbb R^2$.
104369
If $f$ continuous and $f(x^2) = f(x)$, then $f$ is a const
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
122160
$f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$?
47
Let $f$ be a continuous and open map from $\mathbb R $ to $\mathbb R$.Prove that $f$ is monotonic.
136056
$ f:\mathbb C\rightarrow \mathbb C$ defined by $f(z)=0$, if $Re(z)=0$ or $Im(z)=0$ and $f(z)=z$, otherwise.
139744
For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
83338
Show that there's no continuous function that takes each of its values $f(x)$ exactly twice.
47419
Asymptotics of uniformly continuous functions over $\mathbb R$
9406
Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
76009
Can a continuous function from the reals to the reals assume each value an even number of times?
44144
If $f:[a,b]\to \mathbb R$ is continuous then so is $\max_{t\in [a,x]}f(t)$?
145919
If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.