Show that the image of the function $f:(0,\infty)\rightarrow \mathbb{R}$, $f(x)=x+\frac1x$ is the interval $[2,\infty)$.
44233
How to prove this inequality $ x + \frac{1}{x} \geq 2 $
98772
Continuity of a function in $\mathbb{R}$
137043
To show that function is constant
117418
Showing that the image of a function is $\mathbb{C}$ if it satisfies a nice functional equation
141423
The continuity of $f(x,y) = \frac {\sin (xy)} {\sqrt {x^2 + y^2}}$ at $(0,0)$
77943
If $f$ is continuous, then there exists $x+\frac{1}{n}\in[0,1]$ and $f\left(x+\frac{1}{n}\right)=f(x)$
65753
The Function $f:\mathbb{R}^{2}\rightarrow \mathbb{R}^{2}$ defined by $f(r,\theta)=(r\cos\theta,r\sin\theta)$
22210
Points of discontinuity of a bijective function $f:\mathbb{R} \to [0,\infty)$
101267
Show: $\int f\, d\mu=\int\limits_0^{\infty}\mu(\left\{x\in X: f(x)>t\right\})\, dt$
48314
Show that if a function is not negative and its integral is $0$ than the function is $0$
16775
Showing that $\int_{0}^{\infty} \frac{dx}{1 + x^2} = 2 \int_0^1 \frac{dx}{1 + x^2}$
95921
Question about $\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}$
95970
Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$
50103
Show that a continuous function satisfying $f(2^x)=f(3^x)$ for $x\in (0,\infty)$ is a constant function
13747
Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$
74258
Show that $(1+\frac{x}{n})^n \rightarrow e^x$ uniformly on any bounded interval of the real line.
8829
How to prove $\int_{-\infty}^{+\infty} f(x)dx = \int_{-\infty}^{+\infty} f\left(x - \frac{1}{x}\right)dx?$