All Tasks

Inverse arccotan

Consider $a=tg(arccot(\sqrt(2))$. So the value of $a$ is:
 
# Functions of one variable

Training
13

Inverse function with arccotan

Consider the function $f(x)=\dfrac{2\pi}{5}\text{arccot}\left(\ln(x+1)\right)$. The inverse functions of $f$, its domain ($D_{f^{-1}}$) and its range ($D'_{f^{-1}}$) are, respectively:
 
# Unassigned

Training
13

Inverse arccotan

Let $f$ be the function defined by $f(x) =\pi-arccot(2x)$. So the inverse of $f$, $f^{-1}$, is the function defined by
 
# Functions of one variable

Training
13

Inverse of a function with arccotan

The expression of the inverse function of $f(x)=2\text{arccot}(x+1)$ is:
 
# Functions of one variable

Training
13

Inverse of a function with arccotan

The inverse function of the fucntion $f(x)=-\dfrac{3\pi}{2}\text{arccot}\left(\dfrac{2x+1}{3}\right)$ is:
 
# Functions of one variable

Training
13

Domain and range of arccotan

Determine the domain of the function $f(x)=\text{arccot}\left(e^{\sqrt{x}}\right)$. Calculate the value of $k\in R$ for which the range of the function $g(x)=\dfrac{k}{2}\left|f(x)-\pi\right|$ is $\left]\dfrac{3\pi}{2},2\pi\right[$.
 
# Unassigned

Training
13