How to solve this limit?

Question

Given: g(x) = 1/x^2-4 and f(x) = √(x+7), find lim(f(g(x)) as x--> 2

Answer 1

Given g(x) = 1/x^2 -4 and f(x) = √(x+7) then

f(g(x)) = f(1/x^2 -4)

         =√(1/x^2 -4+7)

         =√(1/x^2 +3)

Now

 Lt   f(g(x))   =   Lt    √(1/x^2 +3)

x→2               x→2

Substitute  x = 2

                  =   √(1/2^2 +3)

                  =   √(1/4 +3)

                  =   √(1+12/4)

                  =   √(13/4)

The solution of  Lt   f(g(x))  is  √(13/4).

                     x→2