Let f(x) = x^2 + 6 and g(x) = x+8/x . find ( g o f)(­ -7)

One way to approach this is to find (g o f)(x) first and then to replace x by -7:

g( f(x) ) = (x^2+6) + 8/(x^2+6)

Now replace x with -7.  We get:    ( g o f )(-7) = 49+6+8 / (49+6), or
                                                                        = 55 + 8 / 55, or 55 8/55 (ans.)