1003019401
Level:
C
Identify which of the given functions is even.
\( m(x)=\frac{x^4-3}{x^2} \)
\( h(x)=\frac{x^3+2}{x^2} \)
\( g(x)=\frac{x^2}{x+1} \)
\( f(x)=\frac{x^3}{x^2-5} \)
C
1003025504
Level:
C
Find the range of the function \( f(x)=\Bigl|\left(\frac13\right)^x-1\Bigr|\).
\( [ 0;\infty) \)
\( ( 0;\infty) \)
\( (-1;\infty) \)
\( [ -1;\infty) \)
1003025503
Level:
C
Find the domain of the function \( f(x)=\sqrt{3^x}\).
\( (-\infty;\infty) \)
\( (0;\infty) \)
\( [0;\infty) \)
\( (-\infty;0) \)
1103025502
Level:
C
Identify a possible graph of the function \( f(x)=\Bigl|\left(\frac12\right)^x-1\Bigr|\).
1103025501
Level:
C
Identify a possible graph of the function \( f(x)= 2^{|x|}-1\).
1003020901
Level:
C
Let there be vectors: \(\vec{a}=(1;3;-1)\), \(\vec{b}=(0;3;1)\), \(\vec{c}=(-1;2;2)\). Find \(\vec{a}\times\vec{b}\) and \(\left(\vec{a}\times\vec{b}\right)\cdot\vec{c}\).
\(\vec{a}\times\vec{b}=(6;-1;3); \left(\vec{a}\times\vec{b}\right)\cdot\vec{c}=-2\)
\(\vec{a}\times\vec{b}=8; \left(\vec{a}\times\vec{b}\right)\cdot\vec{c}=(-8,16,16)\)
\(\vec{a}\times\vec{b}=(-6;1;-3); \left(\vec{a}\times\vec{b}\right)\cdot\vec{c}=2\)
\(\vec{a}\times\vec{b}=\sqrt{46}; \left(\vec{a}\times\vec{b}\right)\cdot\vec{c}=2\)
9000153901
Level:
C
Find the number of ways how to distribute
\(8\) identical
balls among \(5\)
persons so that each of them gets at least one ball.
\(\left({7\above 0.0pt
3}\right) = 35\)
\(5^{3} = 125\)
\(\left({12\above 0.0pt
5} \right) = 792\)
\(\left({12\above 0.0pt
8} \right) = 495\)
9000153902
Level:
C
Find the number of ways how to distribute
\(8\) identical
balls among \(5\)
persons.
\(\left({12\above 0.0pt
8} \right) = 495\)
\(5^{8} = 390625\)
\(\left({8\above 0.0pt
5}\right) = 56\)
\(\left({12\above 0.0pt
5} \right) = 792\)
9000153905
Level:
C
Find the number of ways how to distribute
\(5\) identical
balls among \(8\)
persons.
\(\left({12\above 0.0pt
5} \right) = 792\)
\(8^{5} = 32768\)
\(\left({12\above 0.0pt
8} \right) = 495\)
\(\frac{8!}
{3!} = 6720\)
9000153907
Level:
C
Find the number of ways how to distribute
\(5\) different
balls among \(8\)
persons.
\(8^{5} = 32\:768\)
\(\left({12\above 0.0pt
5} \right) = 792\)
\(\frac{8!}
{3!} = 6\:720\)
\(\frac{8!}
{5!3!} = 56\)