2010014503
Level:
C
Identify which of the following points lies on the graph of the inverse of function \( f(x)=x^3-3\).
\( [24;3] \)
\( [-24;-3] \)
\( [-24;3] \)
\( [24;-3] \)
\( [3;24] \)
Properties of Functions
2010014502
Level:
B
Let \( f(x)=\frac{\sqrt{x-3}}{x^2-16} \). Which of the statements about the domain of the function \( f \) is true?
\( D(f)=[ 3; 4)\cup (4;\infty) \)
\( D(f)=(3; 4)\cup (4;\infty) \)
\( D(f)=(-\infty; -4)\cup (3;4) \)
\( D(f)=(-4; 3)\cup (4;\infty) \)
2010014501
Level:
A
Suppose each of the following tables defines function \( f \) completely. Identify which of the tables represents an even function.
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-5&-3& -2&0&2&3&5 \\\hline f(x) &2&-3&1&0&1&-3&2\\ \hline\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-5&-3& -2&0&2&3&5 \\\hline f(x) &2&-3&1&0&-1&3&-2\\ \hline\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-3&-2& -1&0&1&2&3 \\\hline f(x) &-3&-2&-1&1&1&2&3\\ \hline\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-3&-2& -1&1&2&3&4 \\\hline f(x) &2&-3&1&-1&3&2&4\\ \hline\end{array}\)
211011802
Level:
A
Identify a possible graph of an odd function.
211011801
Level:
A
Identify a possible graph of an even function.
2000005202
Level:
C
From the given functions select a function \(f\) so that its inverse function \(f^{-1}\) has the graph shown in the picture.
\( f(x) = \sqrt{x+1};~x\in[ -1;\infty) \)
\( f(x) = x^2-1;~x\in (-\infty;0]\)
\( f(x) = \frac{1}{\sqrt{x-1}};~x\in[ -1;\infty) \)
\( f(x) = x^2-1;~x\in\ \mathbb{R} \)
2000005201
Level:
C
Which of the following functions is the inverse function to the function \(f(x)=-3x+2\)?
\( f^{-1}(x)=-\frac{x}{3}+\frac{2}{3}\)
\( f^{-1}(x)=\frac{x}{3}-\frac{2}{3}\)
\( f^{-1}(x)=2x-3\)
\( f^{-1}(x)=-\frac{x}{3}+1\)
2000005108
Level:
A
Which of the following statements about the function \(f\) is correct? (See the picture.)
The function is one-to-one.
\(D(f)=(-4;\infty)\) and the function is bounded below.
The function has a local maximum.
The function is odd.
2000005107
Level:
A
Which of the following statements about the function \(f\) is correct? (See the picture.)
The function is bounded below.
\( H(f)=(-2;2) \)
The function is even.
The function is increasing on the interval \( (2;\infty)\).
2000005106
Level:
A
Which of the following statements is not valid for the function \(f\)? (See the picture.)
The function is one-to-one.
The function is bounded below.
\(f(-1) =2\).
The value \(-2\) doesn’t belong to the range of \(f\).