Question

Sum difference and product of two functions

Answer 1

1)
`(g+h)(x)=4x^2+x+2`

2)
`(g-h)(x)=-4x^2+x+2`

3)
`(g\bullet h)(-3)=-36`

Explanation:

The given functions are

`g(x)=x+2`

and

`h(x)=4x^2`

1)
`(g+h)(x)=g(x)+h(x)`

This implies that;

`(g+h)(x)=x+2+4x^2`

Rewrite in standard form to obtain
`(g+h)(x)=4x^2+x+2`

2)
`(g-h)(x)=g(x)-h(x)`

This implies that;

`(g-h)(x)=x+2-4x^2`

Rewrite in standard form to obtain
`(g+h)(x)=-4x^2+x+2`

3)
`(g\bullet h)(x)=(x+2)(4x^2)`

We now substitute
`x=-3` to obtain;

`(g\bullet h)(-3)=(-3+2)(4(-3)^2)`

`(g\bullet h)(-3)=(-1)(36)`

`(g\bullet h)(-3)=-36`