#### 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 $\left]\dfrac{3\pi}{2},2\pi\right[$.

# Functions of one variable

Training
13

#### Domain arccotan

Consider the function $f$ defined by $f(x)=\pi-arccot(2x)$. Then the domain, D, and the range of values, $D^{\prime}$ are:

# Functions of one variable

Training
13

#### Domain and range of arccotan

The domain ($D_f$) and the range ($D^{\prime}_f$) of the function $f(x)=2\text{arccot}(x+1)$ are, respectively:

# Functions of one variable

Training
13

#### Domain and range of arccotan

The domain ($D_f$) and the range ($D^{\prime}_f$) of the function $f(x)=\pi^2-\dfrac{3\pi}{2}\text{arccot}\left(\dfrac{2x+1}{3}\right)$ are, respectively:

# Functions of one variable

Training
13