College Level Algebra Solutions

1. Find the LCD:  a(a + 1)
   Rewrite each term with the same LCD and add:
      
   

    

2. Find the Least Common Denominator of:  
   Factor each denominator:
   x² + x = x (x + 1)
   x² - 1 = (x + 1) (x - 1)
   x³ - x = x(x² - 1) = x (x + 1) (x - 1)
   The LCD is the product of the underlined factors:   x(x + 1)(x - 1)
    
    
3. Multiply the numerator and denominator by a and simplify:
   
   

    

4. The given graph is a graph of the parabola y = x² that has been translated to the left by 2 units and downward by 3 units.
   A general equation for a parabola with its vertex at (h, k) is:  y = (x - h)² + k
   Equation is:  y = (x - (-2))² - 3
   Final answer:  y = (x + 2)² - 3
    
    
5. Find one of the solutions to the quadratic equation:  x² - 4x + 5 = 0
   Use the quadratic formula to solve the quadratic equation
   
   a = 1,  b = -4,  c = 5
   
   
   From the choices given, the final answer is:  2 + i

     

6. Given:  f(x) = 2x² - x + 1
   Find:    f(x^½)
   

      

7. Given:  f(x) = 3x - 2
   Find:    f ^-1(4)
   Method 1:  Find the inverse function, f ^-1(x) and then evaluate f ^-1(4).
   Method 2:  The range of the original function is the domain of its inverse.
   Therefore, find x when f (x) = 4:
   4 = 3x - 2  and solve for x. 
   x = 2
   Final answer:  f ^-1(4) = 2  because f(2) = 4

    

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