For the given functions f and g find the requested composite

For the given functions f and g, find the requested composite function value. f(x) = 4x + 4, g(x) = 4x^2 + 5; Find (f g)(2). f(x) = x - 6/x, g(x) = x^2 + 9; Find (g f)(-2).

Solution

1.f(x)=4x+4 ,g(x)=4x^2+5

(fog)(2)= f(g(2))

So first we need to find g(2)

g(2)=4(2)^2 + 5= 4(4)+5=21

f(g(2))=f(21)

        = 4(21)+4=88

THerefore fog(2)=88

2. f(x)= (x-6)/x ,g(x)=x^2+9

(gof)(-2)= g(f(-2))

Therefore first we need to find f(-2)

f(-2)= (-2-6)/-2=-8/-2=4

g(f(-2))=g(4)

          = 4^2 + 9=25

Therefore gof(-2)=25