given f(x) =x^2+7 and g (x)=x-4/x find (gof)(-1).

Answer 1

The function f(x) = x² + 7 and g(x) = x - 4/x

First find the (gof)(x)

(gof)(x) = g(f(x))

Substitute the expression for functioning f (in this case x²  + 7 ) for f (x) in the composition.

            = g(x² + 7)

Now substitute this expression (x² + 7) in to function g in place of the x value.

           = (x²  + 7) - 4/(x²  + 7)

          = [(x²  + 7)²  - 4 ]/(x²  + 7)

(gof)(-1) = [((-1)²  + 7)²  - 4 ]/((-1)²  + 7)

              = [(1 + 7)²  - 4 ]/( 1 + 7)

              = [(64 - 4)/8]

              = 60/8

(gof)(-1) = 15/2.