Question

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Answer 1

97.

For finding f(g(x)) we will plugin value of g(x) in place of x in f(x).

99.

Explanation:

Answer 2

93.
`g(n) = n - 4`

`f(n) = 2n^2 - 5n`

then
`g(n) +f(n) = (n-4) + (2n^2 - 5n)`

`= n - 4 + 2n^2 - 5n`

`= 2n^2 -5n + n - 4`

`= 2n^2 - 4n -4`


95.
`f(n) = -n+3`

`g(n) = n^3 + 3n`
Then
`f(n) . g(n) = (-n+3) . (n^3 + 3n)`

`= -n^4 + 3n^3 - 3n^2 + 9n`


97.
`f(x) = 3x+1`

`g(x) = 2x`
For finding f(g(x)) we will plugin value of g(x) in place of x in f(x).

`f(g(x)) = 3*(2x) + 1`

`= 6x + 1`


99.
`f(n) = n - 3`

`g(n) = 2n^2 - 3n`


`g(-7) = 2*(-7)^2 - 3 * (-7) = 2* 49 + 21 = 98 + 21 = 119`

`f(g(-7)) = 119 - 3 = 116`