9000010509
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
x\cdot \root{3}\of{x^{11}}
\]
\(x^{4}\root{3}\of{x^{2}}\)
\(x^{11}\root{3}\of{x}\)
\(x^{12}\root{3}\of{x}\)
\(x\root{3}\of{x}\)
A
9000010605
Level:
A
Identify a function which is decreasing on
\((-\infty ;1)\).
\(f(x) = -x^{3}\)
\(f(x) = -x^{2}\)
\(f(x) = x^{3}\)
\(f(x) = -x^{4}\)
\(f(x)= x^{-2}\)
\(f(x) = x^{2}\)
9000010606
Level:
A
Identify a function which is increasing on
\((-1;3)\).
\(f(x) = (x + 2)^{2}\)
\(f(x) = x^{2} + x\)
\(f(x) = x^{2} - x\)
\(f(x) = (x - 2)^{2}\)
\(f(x) = -x^{3}\)
\(f(x) = x^{2} + 1\)
9000011103
Level:
A
In the following list identify an increasing function.
\(f(x) = x^{5}\)
\(f(x) = x^{2}\)
\(f(x) = x^{-3}\)
\(f(x) = x^{-4}\)
\(f(x) = 2x^{0}\)
9000010607
Level:
A
Identify a function which is one-to-one on the interval
\([ - 2;2] \).
\(f(x) = x^{3} - 2\)
\(f(x) = x^{2} - 2\)
\(f(x) = -x^{2} + 2\)
\(f(x) = x^{-2} + 2\)
\(f(x) = \frac{1}
{x} - 2\)
\(f(x) = x^{4}\)
9000008002
Level:
A
Consider the point \(A = [-1;-3]\) and
the function \(f(x) = \frac{k}
{x}\) with a nonzero
real parameter \(k\in \mathbb{R}\setminus \{0\}\). Identify
the value of the parameter \(k\)
which ensures that the point \(A\)
is on the graph of \(f\).
\(3\)
\(1\)
\(- 1\)
\(- 3\)
9000008003
Level:
A
Given the function \(f(x) = \frac{6}
{x}\),
solve the following equation.
\[
f(x) = 2
\]
\(3\)
\(2\)
\(- 2\)
\(- 3\)
9000008004
Level:
A
Given the function \(f(x) = -\frac{8}
{x}\),
evaluate \(f(-4)\).
\(2\)
\(- 4\)
\(4\)
\(32\)
9000008006
Level:
A
Given the functions \(f(x) = \frac{2}
{x}\)
and \(g(x) = \frac{4}
{x}\),
identify a true statement.
\(f(2) = g(4)\)
\(f\left (\frac{1}
{2}\right ) = g(2)\)
\(f(1) > g(2)\)
\(f(4) < g(10)\)
9000008007
Level:
A
Given the functions \(f(x) = -\frac{3}
{x}\)
and \(g(x) = 6\),
solve \(f(x) = g(x)\).
\(-\frac{1}
{2}\)
\(- 2\)
\(3\)
\(6\)