1003164104
Level:
B
Let \( f(x)=\sqrt x \) and \( g(x)=\sqrt[3]x \). Identify which of the following statements is true.
\( \frac{g(48)}{g(6)} =2 \)
\( f(15)+g(17)=2 \)
\( f(2)\cdot g(16)=2 \)
\( f(11)-f(7)=2 \)
Power and radical functions
1003164103
Level:
B
Let \( f(x)=\sqrt[4]x \). Identify which of the following statements is false.
\( f\!\left(\sqrt5\right)=\sqrt[6]5 \)
\( f\!\left(\sqrt[3]{81}\right)=\sqrt[3]3 \)
\( f(49)=\sqrt7 \)
\( f\!\left(\frac{25}{256}\right)=\frac{\sqrt5}4 \)
1003164102
Level:
B
Let \( f(x)=\sqrt[3]x \). Identify which of the following statements is true.
\( 2\cdot f(5)=\sqrt[3]{40} \)
\( f(0.27)=0.3 \)
\( f\!\left(\frac13\right)=\frac{\sqrt[3]3}3 \)
\( f(504)=6\cdot\sqrt[3]7 \)
1003164101
Level:
B
Let \( f(x)=\sqrt x \). Identify which of the following statements is false.
\( f(0.144)=0.12 \)
\( f(48400)=220 \)
\( f\!\left(\frac15\right)=\frac{\sqrt5}5 \)
\( f(588)=14\cdot\sqrt3 \)
1103163103
Level:
A
The parts of the graphs represent the functions: \( f(x)=x^{-2} \), \( g(x)=x^{-3} \), \( h(x)=x^{-4} \).
Choose the legend which assigns the correct color of the graph to each of the given functions.
\( f \) -- green, \( g \) -- blue, \( h \) -- red
\( f \) -- red, \( g \) -- blue, \( h \) -- green
\( f \) -- green, \( g \) -- red, \( h \) -- blue
\( f \) -- blue, \( g \) -- green, \( h \) -- red
1103163102
Level:
A
Function \( f \) is given by the graph.
Identify which of the following statements is true.
\( f(x)=(x+1)^{-3};\ x\in[-3;-1.5] \)
\( f(x)=-(x+1)^{-2};\ x\in[-3;-1.5] \)
\( f(x)=(x+1)^{-5};\ x\in[-3;-1.5] \)
\( f(x)=(x+1)^{-1};\ x\in[-3;-1.5] \)
1103163101
Level:
A
Function \( f \) is given by the graph. Identify which of the following statements is true.
\( f(x)=2+(x-1)^{-2};\ x\in[1.5;6] \)
\( f(x)=2+(x-2)^{-2};\ x\in[1.5;6] \)
\( f(x)=2+(x-1)^2;\ x\in[1.5;6] \)
\( f(x)=2+(x-1)^{-1};\ x\in[1.5;6] \)
1103161003
Level:
A
The graphs represent the parts of the functions \( f(x)=x^{-2} \) and \( g(x)=x^{-3} \). Identify which of the following inequalities has the solution set \( (-\infty;-1)\cup(0;\infty) \).
\( -x^{-3} < x^{-2} \)
\( \left|x^{-3}\right| < x^{-2} \)
\( x^{-3} < -x^{-2} \)
\( x^{-3} < \left|x^{-2}\right| \)
1103161002
Level:
A
The graphs represent the parts of the functions \( f(x)=x^{-2} \) and \( g(x)=x^{-4} \). Identify which of the following inequalities has the solution set \( (-\infty; -1]\cup[1;\infty) \).
\( x^{-4} \leq x^{-2} \)
\( x^{-2} \leq x^{-4} \)
\( x^{-2} > x^{-4} \)
\( x^{-2} < 1 \)
1103161001
Level:
A
The graphs represent the parts of the functions \( f(x)=x^{-2} \) and \( g(x)=x^{-3} \). Identify which of the following statements is false.
The solution set of the inequality \( x^{-2} > 0 \) is \( (-\infty;\infty) \).
The solution set of the inequality \( x^{-3} > 0 \) is \( (0;\infty) \).
The solution set of the equation \( x^{-3} = x^{-2} \) is \( \{1\} \).
The solution set of the inequality \( x^{-3} < x^{-2} \) is \( (-\infty;0)\cup(1;\infty) \).