All Tasks
Solvable or not?
Which of the following equations is not solvable?
# Linear equations
Reasoning
9
Inverse function of arcsin
Consider $f(x)= a -2 \arcsin(1-2x)$ with domain $D_f=[0,1]$ and range $D'_f = \left[ 0, 2\pi\right] $.
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 $f^{-1}(0)=0$.
# Functions of one variable
Training
13
Find the coefficients of terms in algebraic expression_2
Find the number $a$ if the following algebraic expression is independent of $y$.
$A= a(x+y+2)-2(x+2y)+6$
# Linear equations
Reasoning
8
Find the value_1
Evaluate the following algebraic expression if $x=-2$ and $y=-3$
$A=\frac{x+3}3-2\frac{y+2}5$
# Equations & Inequations
Training
8
Simplification of algebraic expression_1
If we simplify the following algebraic expression $A= 2x+3y+7-3x+5x-3+7y$ into the form $ax+by+c$, where the $a,b$ and $c$ are rational numbers, the A is
# Linear equations
Training
8
Chain rule arcsin
Determine the equation of the normal line to the graph of $y(x)=6\arcsin(f(x))$ at $x=0$, knowing that $f(0)=0.5$ and $f'(0)=1$
# Functions of one variable
Reasoning
13