1003159001
Level:
B
Solve.
\[ 5^{-x}=7 \]
\( x=-\log_57 \)
\( x=-\log_75 \)
\( x=\log_57 \)
The equation has no solution.
B
1003164105
Level:
B
Let \( f(x)=\sqrt{x^2} \) and \( g(x)=x \). Identify which of the following statements is true.
\( f(-3)=3 \)
\( f(-5)=-5 \)
\(\forall x \in \mathbb{R}: f(x)=g(x) \)
\(\forall x \in \mathbb{R}: f(x)=-g(x) \)
1003164104
Level:
B
Let \( f(x)=\sqrt x \) and \( g(x)=\sqrt[3]x \). Identify which of the following statements is true.
\( \frac{g(48)}{g(6)} =2 \)
\( f(15)+g(17)=2 \)
\( f(2)\cdot g(16)=2 \)
\( f(11)-f(7)=2 \)
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.
\( f(0.144)=0.12 \)
\( f(48400)=220 \)
\( f\!\left(\frac15\right)=\frac{\sqrt5}5 \)
\( f(588)=14\cdot\sqrt3 \)
1003085810
Level:
B
Let \( x\in\left(\frac{\pi}2,\pi\right] \). Which of the following statements is true?
\( \sin x \geq \mathrm{tg}\,x \)
\( \sin x > \mathrm{tg}\,x \)
\( \sin x < \mathrm{tg}x \)
\( \sin x \leq \mathrm{tg}\,x \)
1003085809
Level:
B
Which of the following inequalities has no solution for \( x\in\mathbb{R} \)?
\( 99\cos x >100 \)
\( \cos^2x -\sin^2x \geq 1 \)
\( \sin|x| < 0 \)
\( \sin 2x \leq 2 \)
1003085808
Level:
B
Which of the following inequalities has no solutions for \( x\in\mathbb{R} \)?
\( \cos^2x -\sin^2x > 1 \)
\( 100\sin x > 1 \)
\( \sin x \cdot \cos x \geq \frac12 \)
\( |\sin x| \geq 1 \)
1003085807
Level:
B
For which \( x\in\left(-\frac{\pi}2,\ \frac{\pi}2\right) \) is the inequality \( \mathrm{tg}\,3x < -1 \) true?
\( x\in\left(-\frac{\pi}2,-\frac{5\pi}{12}\right)\cup\left(-\frac{\pi}6,-\frac{\pi}{12}\right)\cup\left(\frac{\pi}6,\frac{\pi}4\right) \)
\( x\in\left(-\frac{\pi}6,-\frac{\pi}{12}\right)\cup\left(\frac{\pi}6,\frac{\pi}4\right) \)
\( x\in\left(-\frac{\pi}2,-\frac{5\pi}{12}\right)\cup\left(-\frac{\pi}6, - \frac{\pi}{12}\right) \)
\( x\in\left(-\frac{\pi}6, -\frac{\pi}{12}\right)\cup\left(\frac{\pi}{12},\frac{\pi}6\right)\cup\left(\frac{\pi}6,\frac{\pi}4\right) \)