Question

Let f ( x ) = x 2 and g ( x ) = x + 6 , find: a . ( f ∘ g ) ( x ) = b . ( g ∘ f ) ( x ) = c . ( f ∘ g ) ( − 3 ) = d . ( g ∘ f ) ( − 3).

Answer 1

`(fog)(x)=x^2+12x+36`

`(gof)(x)=x^2+6`

`(fog)(-3)=9`

`(gof)(-3)=15`

Explanation:

`f(x)=x^2`

`g(x)=x+6`

`(fog)(x)= f(g(x))`

Plug in g(x)

`(fog)(x)= f(g(x))=f(x+6)`

replace x+6 for x in f(x)

`(fog)(x)= f(g(x))=f(x+6)=(x+6)^2=x^2+12x+36`

`(fog)(x)=x^2+12x+36`

`(gof)(x)= g(f(x))`

`(gof)(x)= g(f(x))=g(x^2)=x^2+6`

`(gof)(x)=x^2+6`

`(fog)(-3)=(-3)^2+12(-3)+36=9`

`(gof)(-3)=(-3)^2+6=15`