Simplify: \( 9^{\log_{9}(4)} = \)
A. 3 B. 4 C. 9 D. 81
Question 2
Simplify: \( 3^{\log_{3}(-5)} = \)
A. -5
B. 3 C. 9 D. undefined
Question 3
If \( f(x) = -2x^{2} + 8x - 4 \), which of the following is true?
A. The maximum value of \( f(x) \) is - 4. B. The graph of \( f \) opens upward. C. The graph of \( f \) has no x-intercept D. \( f \) is not a one to one function.
Question 4
If \( f(x) = 5 - 2^{x} \), then \( f^{-1}(- 3) = \)
A. \( \dfrac{8}{39} \) B. -3 C. 3 D. 32
Question 5
If \( \log_{x}(3) = \dfrac{1}{4} \), then \( x = \)
A. 81 B. \( \dfrac{1}{81} \) C. 3 D. 9
Question 6
If \( f(x) = -x^{2} + 1 \), then \( f(x + 1) = \)
A. \( -x^{2} + 1 \) B. \( -x^{2} - 2x \) C. \( -x^{2} \) D. \( -x^{2} -2x - 2 \)
Question 7
If \( f(x) = x - 4 \), then \( (f_{o}f)(3) = \)
A. 1 B. -1 C. -5 D. 5
Question 8
If \( \ln(3x - 2) = 1 \), then \( x = \)
A. \( \dfrac{2}{3} \) B. \( \dfrac{(2 + e)}{3} \) C. \( \dfrac{3}{2} \) D. \( \dfrac{e}{3} \)
Question 9
The number of solutions of \( (x^{2} + 1)^{2} + 2(x^{2} + 1) - 3 = 0 \) is equal to
A. 1 B. 2 C. 3 D. 4
Question 1o
If the graph of \( y = (x - 2)^{2} - 3 \) is translated 5 units up and 2 units to the right, then the equation of the graph obtained is given by
A. \( y = x^{2} + 2 \)
B. \( y = (x - 2)^{2} + 5 \)
C. \( y = (x + 2)^{2} + 2 \)
D. \( y = (x - 4)^{2} + 2 \)
Question 11
If \( f(x) = -e^{x} - 2 \), then the range of \( f \) is given by the interval
A. \( (-\infty , -2) \) B. \( (-\infty , +\infty) \)
C. \( (-2; , +\infty) \) D. \( (-\infty , +2) \)
Question 12
If \( f(x) = \dfrac{\sqrt{x - 1}}{x^{2} - 9} \), then the domain of \( f \) is given by the interval
A. \( (1 , +\infty) \) B. \( (-3 , +3) \)
C. \( [1 , 3) \cup (3 , +\infty) \) D. \( (-3 , 3)
\cup (3 , +\infty) \)
Question 13
The number of points of intersections of the graphs of \( y = 2^{x} \) and \( y = -x^{2} + 2 \) is equal to
A. 0 B. 1 C. 2 D. 3
Question 14
If \( f(x) = \ln(x + 1) - 2 \), then \( f^{-1}(x) = \)
A. \( e^{x + 1} - 2 \)
B. \( e^{x} - 2 \)
C. \( e^{x + 2} - 2 \) D. \( e^{x + 2} - 1 \)
Question 15
For all \( x \) real, \( \sqrt{x^{2} -4x + 4} = \)
A. \( x - 2 \) B. \( x + 2x + 2 \)
C. \( |x - 2| \) D. \( x + 2 \)
Question 16
The value of \( x \) that makes \( x^{2} + 6x + 13 \) maximum is equal to
A. 6 B. -3
C. 13 D. 3
Question 17
\( e^{\ln(3) - \ln(2) + \ln(1/x)} = \)
A. \( \dfrac{3}{2x} \) B. \( \dfrac{3x}{2} \)
C. \( 1 + \dfrac{1}{x} \) D. \( \dfrac{3}{2} - \dfrac{1}{x} \)
Question 18
If \( f(x) = \dfrac{x - 1}{x + 2} \), then the range of \( f \) is given by the interval
A. \( (-\infty , -2) \cup (-2 , +\infty) \) B. \( (-\infty , 1) \cup (1 , +\infty) \)
C. \( (-2; , +\infty) \) D. \( (-\infty , 1) \)
Question 19
\( \ln((x - 1)^{2}) = 2 \ln(x - 1) \) for all \( x \) in the interval
A. \( (-\infty , +\infty) \) B. \( [0 , +\infty) \)
C. \( (-\infty , 1) \cup (1 , +\infty) \) D. \( (1 , +\infty) \)
Question 20
Let \( f(x) = x^{2} + 2x + 4 \). Which of the following statements is NOT true?
A. \( f(x) \) has a maximum value B. The graph of \( f \) is not a line
C. The graph of \( f \) has no x-intercepts. D. The graph of \( f \) has a y-intercept.
