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

Answer:

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

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

$(fog)(-3)=9$

$(gof)(-3)=15$

Step-by-step 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)

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

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

$(gof)(x)= g(f(x))$

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

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

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

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