Logarithmic functions

9000004905

Level: 
C
In the following list identify a statement which is not true for the function \(f\colon y = |\log (x - 3) - 1|\).
The function \(f\) is increasing on the domain.
The domain of the function \(f\) is \((3;\infty )\).
All values of the function \(f\) are nonnegative.
The function \(f\) does not have a \(y\)-intercept.
The \(x\)-intercept of the function \(f\) is \(x = 13\).
The function \(f\) is not one-to-one.

9000033705

Level: 
C
Find the domain of the following function. \[ f(x) = \sqrt{\log (x^{2 } + 2x + 1)} \]
\(\left (-\infty ;-2] \cup [ 0;\infty \right )\)
\(\mathbb{R}\setminus \left \{-1\right \}\)
\(\left (-1;\infty \right )\)
\(\left (-\infty ;-1\right )\cup \left (1;\infty \right )\)
\(\left (-\infty ;0\right )\cup \left (2;\infty \right )\)