Continuity of function if $f^2$ and $f^3$ are continuous
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 $\mathbb{R}$
150554
proof that $f'$ is continuous at $a$
153730
Show that $f(x)=x^2$ is continuous at $a=2$ using the $\delta-\epsilon$ definition of continuity.
145368
How to show $f:Y\to X^{+}$ is continuous?
141938
Find all continuous functions from positive reals to positive reals such that $f(x)^2=f(x^2)$
108057
If $(f_n)\to f$ uniformly and $f_n$ is uniformly continuous for all $n$ then $f$ is uniformly continuous
5419
Continuous functions with $f^2(x)=g^2(x)\neq 0$
130299
Prove that if a function $f: X\to Y$ continuous then its graph is closed
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 $a$
151427
f, g continuous for all rationals follow by continuous on all reals?
139744
For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
72044
prove $x \mapsto x^2$ is continuous
2357
Showing $\frac{x^3y}{x^4+y^2}$ is continuous at all points
143174
property of continuous function
15914
Prove that any polynomial function is continuous
147299
Prove that $g(x,y) = \frac{x^3y}{x^2+y^2}$ with $g(0,0)=0$ is continuous
51156
Function is Continuous When Restricted to Closed Sets Which Cover the Space