functions and graphs 8

Mathematics
Tutor: None Selected Time limit: 1 Day

i am stuck on the following problem. here is a pic of the problem

http://imgur.com/8SkodmK

Nov 18th, 2014

f(x) - f(a) / x - a

f(x) = x^2 - 4x + 5        a = - 2

f(a) = (a)^2 - 4(a) + 5

      = a^2 - 4a + 5

Now putting the values in the above relation , we get

f(x) - f(a) / x - a = (x^2 - 4x + 5) - (a^2 - 4a + 5) / x - a

                         = x^2 - 4x + 5 - a^2 + 4a - 5 / x - a

                        = x^2 - a^2 - 4x + 4a + 5 - 5 / x -a

                        = (x - a)(x+a) - 4(x + a) / x -a

             Hence    

                                 f(x) - f(a) / x - a    =    (x - a)(x+a) - 4(x + a) / x -a

Nov 18th, 2014

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