Question

The function f is defined by f(x) = (x − 2) 2 − 3 for x > −2. The function g is defined by g(x) = 2x+6 x−2 for x > 2. Find fg(7).

Answer 1

`fg(7)=143.95`

Explanation:

We are given that

`f(x) = (x -2)^2 -3` for x > −2

`g(x) = 2x+6x^(-2)` for x > 2

We have to find fg(7)

`fg(7)=f(g(7))`

`=f(2(7)+6(7)^(-2))`

=
`f(14+(6)/(49))`

=
`f((692)/(49))`

692/49>-2

fg(7)=
`((692)/(49)-2)^2-3`

=
`146.95-3`

Hence,
`fg(7)=143.95`