Question 1135884


Let {{{f (x) = 3x^2 - x - 7 }}}and {{{g(x) = 3x - 1 }}}

(a) Determine the composite function (f ∘ g)(x) and simplify the results. Show work. 

(f ∘ g)(x) ={{{f(g(x))}}}

(f ∘ g)(x) ={{{f(3x - 1)}}}

(f ∘ g)(x) ={{{3(3x - 1)^2 - (3x - 1) - 7}}}

(f ∘ g)(x) ={{{3(9x^2 - 6x+1) - 3x +1 - 7}}}

(f ∘ g)(x) ={{{27x^2 - 18x+3 - 3x +1 - 7}}}

(f ∘ g)(x) ={{{27x^2 - 21x - 3}}}


(b) Compute (f ∘ g)(-1) . 

(f ∘ g)(-1) ={{{27(-1)^2 - 21(-1) - 3}}}

(f ∘ g)(-1) ={{{27 +21 - 3}}}

(f ∘ g)(-1) ={{{45}}}