Rational functions

1003124601

Level: 
B
Let \( f(x)=\frac{2x}{x^2-1} \). Find the true statement.
\( \forall x\in(-\infty;-1)\cup(0;1)\colon f(x) < 0 \).
The domain of \( f \) is \( (-\infty;1)\cup(1;\infty) \).
\( \forall x\in(-1;1)\colon f(x) \leq 0 \).
The domain of \( f \) is \( (-\infty;-1)\cup(-1;0)\cup(0;1)\cup(1;\infty) \).

1003118306

Level: 
C
Find the true statement about the function \( f(x)=\left|\frac{4x-4}{2x-1}\right| \).
The domain of the function \( f \) is the set \( \left(-\infty;\frac12\right)\cup\left(\frac12;\infty\right) \).
The range of the function \( f \) is the set \( [0;2)\cup(2;\infty) \).
The function \( f \) has the minimum at \( x=4 \).
The function \( f \) is an injective (one-to-one) function.

1003118305

Level: 
C
Find the false statement about the function \( f(x)=\left|\frac1{2-3x}-3\right| \).
The domain of the function \( f \) is the set \( \left(-\infty;\frac32\right)\cup\left(\frac32;\infty\right) \).
The range of the function \( f \) is the interval \( \left[0;\infty\right) \).
The function \( f \) has the minimum at \( x=\frac59 \).
The function \( f \) is bounded below.