A set of college algebra multiple choice questions, with answers, are presented. The answers are at the bottom of the page. Also Detailed solutions with full explanations are included.

9^{log9(4)} =

3^{log3(5)} =
A. 5 
B. 3 
C. 9 
D. undefined 

If f(x) = 2x^{2} + 8x  4, which of the follwoing 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 xintercept 
D. f is not a one to one function. 

If f(x) = 5  2^{x}, then f^{1}(3) =

If log_{x}(3) = 1/4, then x =

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


If f(x) = x  4, then (f_{o}f)(3) = =

If ln(3x  2) = 1, then x =
A. 2/3 
B. (2 + e)/3 
C. 3/2 
D. e/3 

The number of solutions of (x^{2} + 1)^{2} + 2(x^{2} + 1)  3 = 0 is equal to

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


If f(x) = e^{x}  2, then the range of f is given by the interval
A. (∞ , 2) 
B. (∞ , +∞) 




C. (2; , +∞) 
D. (∞ , +2) 

If f(x) = √(x  1) / (x^{2}  9), then the domain of f is given by the interval
A. (1 , +∞) 
B. (3 , +3) 




C. [1 , 3)U(3 , +∞) 
D. (3 , 3)U(3 , +∞) 

The number of points of intersections of the graphs of y = 2^{x} and y = x^{2} + 2 is equal to

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


For all x real, √(x^{2} 4x + 4) =
A. x  2 
B. x + 2x + 2 




C. x  2 
D. x + 2 

The value of x that makes x^{2} + 6x + 13 maximum is equal to

e^{ln(3)  ln(2) + ln(1/x)} =
A. 3 / (2x) 
B. 3x/2 




C. 1 + 1/x 
D. 3/2  1/x 

If f(x) = (x  1) / (x + 2), then the range of f is given by the interval
A. (∞ , 2)U(2 , +∞) 
B. (∞ , 1)U(1 , +∞) 




C. (2; , +∞) 
D. (∞ , 1) 

ln((x  1)^{2}) = 2 ln(x  1) for all x in the interval
A. (∞ , +∞) 
B. [0 , +∞) 




C. (∞ , 1)U(1 , +∞) 
D. (1 , +∞) 

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 xintercepts. 
D. The graph of f has a yintercept. 

