1 find the natural domain of the following

Question

1.  Find the natural domain of the following functions. Explain your results.

2. Given the equation y= x² - 6x +8, find the following:

     (i) For what values of x is y  = - 10?
     (ii) For what values of x is y = ≥ 0 ?
     (iii) Find the minimum value of y.
     (iv) Find the maximum value of y.
 
3.  (a)Sketch the graph of y = x-1/x by translating, reflecting, compressing and stretching the graph of y =1/x

     (b) Find an expression for f o g, given that:

 4. Find the equation of all lines passing through the point (6, -1) for which the product of  their x- and y- intercepts is 3. Sketch these lines.

5. (a) Find the amplitude and period, and sketch at least two periods of the following function: 

       y = 1/2 cos(3x - Π)

      (b)  Express the following expression as a single logarithm:                        

          2ln(x+1) + 1/3 ln(x - cosx)
 
6. Find the expression for:  (i)  ) sin(cos^-1x ) and  (ii) tan(cos^-1x).

 

7. Solve the following equation for x:

8. Find the limit of the following:

9. Find :

 

10. Find