Question

I need help please with this 1 problem

Answer 1

See below, please

Explanation:

We know

`f(x) = {x}^(2) + 3x - 7`

`g(x) = 3x + 5`

`h(x) = 2 {x}^(2) - 4`

Hence

`f(g(x))`

`= {(3x + 5)}^(2) + 3 * (3x + 5) - 7`

`= (9 {x}^(2) + 30x + 25) + (9x + 15) - 7`

`= 9 {x}^(2) + 39x + 33`

`h(g(x))`

`= 2 * {(3x + 5)}^(2) - 4`

`2 * (9 {x}^(2) + 30x + 25) - 4`

`= 18 {x}^(2) + 60x + 50 - 4`

`= 18 {x}^(2) + 60x + 46`

`(h - f)(x)`

`= h(x) - f(x)`

`= (2 {x}^(2) - 4) - ( {x}^(2) + 3x - 7)`

`= {x}^(2) - 3x + 3`

`(f + g)(x)`

`= f(x) + g(x)`

`= ( {x}^(2) + 3x - 7) + (3x + 5)`

`= {x}^(2) + 6x - 2`