Find the function and domain f(x)= 6x + 7, g(x)=x^2 + x (Question a) f o g (f o g)(x)

Question

Find the functions and their domains. (Enter the domains in interval notation.)
f(x) = 6x + 7,

g(x) = x2 + x
(a) f ∘ g
(f ∘ g)(x)  =

b) g o f

(g o f)(x) = 

c)  f ∘ f
(f ∘ f)(x) =

Answer 1

Hi John,

(fog)(x) is easier understood as f[g(x)].   So we are going to use x²+x  in place of every "x" in the f(x) function.

 

f(x²+x) = 6(x²+x) + 7

 

(f o g)(x) = 6x² + 6x +7     

 

The domain is all real numbers since there are no limitations on the domain of f(x) nor of g(x) nor of the composition of f and g.