All Tasks
Equation arctan
Consider $f(x)= \dfrac{\pi}{2} -2 \arctan(1-2x)$ with domain $D_f=\mathbb{R}$.
The solution of the equation $f\left(\dfrac{1}{2}-x \right) + \arctan\left( \dfrac{\sqrt{3}}{3}\right)=\dfrac{\pi}{6}$ is:
# Complements of differential calculus in real numbers
Training
13
Inverse arctan
Consider $f(x)= a -2 \arctan(1-2x), \ a \in \mathbb{R}$, with domain $D_f=\mathbb{R}$.
Determine the analytic expression of the inverse function of $f$, $f^{-1}(x)$, and use that to calculate the value of $a \in \mathbb R$ knowing that $f^{-1}\left( -\dfrac{\pi}{2}\right) =0$.
# Complements of differential calculus in real numbers
Training
13
Domain arctan
The domain ($D_f$) and the range ($D'_f$) of the function
$f(x)=- 2 \left|\dfrac{\pi}{2} -2 \arctan(1-2x)\right| $ are, respectively,
# Complements of differential calculus in real numbers
Training
13
Domain arctan
The domain ($D_f$) and the range ($D'_f$) of the function
$f(x)= -2 \arctan\left(2x\right)$ are, respectively,
# Complements of differential calculus in real numbers
Training
13
Domain arctan
The domain ($D_f$) and the range ($D'_f$) of the function
$f(x)= \dfrac{\pi}{2} -2 \arctan(1-2x)$ are, respectively,
# Complements of differential calculus in real numbers
Training
13
Sum of powers
What is the final value of the following sum:
$ 2^4+3^0+6^2 $
# Powers
Training
8