How do I find the following functions

Question

From   f(x) = 4x − 3, g(x) = 2 − x

 

(a) (f + g)(x) =


(b) (f − g)(x) =


(c) (fg)(x) =


(d) (f/g)(x) =

 

And What is the domain of f/g?

Answer 1

f(x) = 4x − 3, g(x) = 2 − x

     (a) (f + g)(x) = 4x - 3 + 2 - x = 4x - x + 2 - 3 = 3x = 1

     (b) (f − g)(x) = 4x - 3 - (2 - x) = 4x - 3 - 2 + x = 5x - 5

     (c) (fg)(x) = (4x-3)(2-x) = 8x - 4x² - 6 + 3x = -4x² + 11x - 6

     (d) (f/g)(x) = (4x-3)/(2-x) = -4 + (5/(2-x))

 

              _-4___

     -x+2 ) 4x - 3

             -(4x - 8)

             ----------

                      5

     And What is the domain of f/g?  All x except x = 2 (because 2-x = 0 when x = 2, and you can't divide by 0)