Question

Can you please help me find the functions?

Answer 1

`(g+k)(x)=g(x)+k(x) = x-3 + 2x = 3x-3`

`(hk)(x) = h(x)k(x) = (x^2-9)(2x) = 2x^3 - 18x`

`h(g(x)) = h( x-3) = (x-3)^2 -9 = x^2 - 6x`

`h(g(k(x))) = h(g(2x)) = (2x)^2 - 6(2x) = 4x^2 - 12 x`

Answer 2

`f(x)=x`
`g(x)=x-3`
`h(x)=x^2-9`
`k(x)=2*x`

Explanation:

1.
`(g+k)(x)=g(x)+k(x)=`

`=x-3+2*x=3*(x-1)`

2.
`(h*k)(x)=h(x)*k(x)`

`=(x^2-9)*(2*x)=2*x^3-18x`

3.
`h(g(x))=(g(x))^2-9=(x-3)^2-9=`

`=x^2-2*3*x+9-9=x^2-6*x`

4.
We can use the) result of 3. replacing `x` with `k(x)`

`h(g(k(x)))=(k(x))^2-6*k(x)=(2*x)^2-6*2*x=`

`=4*x^2-12x`