Algebra

Algebra Questions With Answers

1. How many x intercepts does the graph of the function f(x) = x ³ + 4 have?
   
   

   A. 0

   B. 1

   C. 2

   D. 3

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2. If Log_b(5) = c, then b ^4c =
   
   

   A. 4

   B. 5

   C. 25

   D. 625

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3. How many points of intersection do the graphs of the functions f(x) = x ² and g(x) = 2 ^x have?
   
   

   A. 1

   B. 2

   C. 3

   D. 4

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4. The range of the function f(x) = -x ² + 2x - 5 is given by
   
   

   A. (0 , infity)

   B. (-infinity , 4]

   C. (-infinity , -4]

   D. (-infinity , -5]

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5. Which of these functions does not have an inverse?
   
   

   A. f(x) = |x - 5|	B. h(x) = 2x - 9
   C. k(x) = ln(- x + 4)	D. j(x) = x 1/3

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6. The solution set of the inequality (x + 5) ⁴(x + 3) ≥ 0 is given by interval
   
   

   A. [-3 , infinity)

   B. {-5} U [-3 , infinity)

   C. (-infinity , infinity)

   D. (-3 , infinity)

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7. The range of the function h(x) = -|x - 5| - 2 is give by
   
   

   A. (-infinity , 0)

   B. (-infinity , -2)

   C. (-infinity , -2]

   D. (-infinity , 2]

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8. 5 ln e ² - 2 ln (7e) + ln 49 =
   
   

   A. 8

   B. 3

   C. 4 ln 7

   D. 8e - 4 ln 7

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9. If f(x) = x / (- x + 4) and g(x) = 2x + 2, then (f ₀ g)(1) =
   
   

   A. 4/3

   B. 4 1/3

   C. 4

   D. undefined

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10. √(x ² + 6x + 9) =
    
    

    A. x + √(6x) + 3

    B. x + 3

    C. |x + 3|

    D. (x + 3) 2

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11. If f(x) = x ² + 1 for x ≤ 0, then f ^-1(x) =
    
    

    A. x -1

    B. √(x - 1)

    C. √(x + 1)

    D. - √(x - 1)

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12. The domain of f(x) = ln(2 - x) + ln(3 - x) is given by
    
    

    A. (-infinity , 2)

    B. (2 , 3)

    C. (-infinity , 3)

    D. (-infinity , 2]

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13. The solution set of the inequality (x - 1) ² ≤ 0 is given by
    
    

    A. (-infinity , infinity)

    B. (-infinity , 1]

    C. {1}

    D. [1 , infinity)

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14. The solution to the equation 2 (4 ^x+1) = 4 (8 ^{x + 2})
    
    

    A. -5

    B. 1

    C. 0

    D. no solution

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15. The number of solutions of the equation | - x ² + 4x + 1 | = 5 is equal to
    
    

    A. 1

    B. 2

    C. 3

    D. 4

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16. Using the absolute value concept, the statement
    
    The distance from x to -6 is not less than 7
    
    may be written as follows
    
    

    A. |x + 6| ≥ 7

    B. |x + 6| > 7

    C. |x + 7| ≥ -6

    D. |x + 7| ≥ 6

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17. If f(2x + 3) = 2x - 1, then f(3x + 4) =
    
    

    A. 6x + 7

    B. 3x

    C. 6x + 11

    D. 9x + 15

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18. -x ² + x - 3 =
    
    

    A. -(x + 1/2)2-11/4

    B. (x - 1/2)2-11/4

    C. -(x - 1/2)2-11/4

    D. -(x - 1/2)2+11/4

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19. How many solutions do the equation 1/x + 1/(x + 1) = 1/3 have?
    
    

    A. 0

    B. 1

    C. 2

    D. 3

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20. If the whole graph of function f lies in quadrant IV, then the graph of the inverse of lies in quadrant
    
    

    A. I

    B. II

    C. III

    D. IV

    
    
    
    Answers to the Above Questions
    1. B
    2. D
    3. B
    4. C
    5. A
    6. B
    7. C
    8. A
    9. D
    10. C
    11. D
    12. A
    13. C
    14. A
    15. C
    16. A
    17. B
    18. C
    19. C
    20. D