If f(x) = 7x - 3 and g(x) = x2, what is (gºf)(1)?Enter the correct answer.
Accepted Solution
A:
Answer:[tex](g\°f)(1)=16[/tex]Step-by-step explanation:Given:[tex]f(x)=7x-3[/tex][tex]g(x)=x^2[/tex]To find composition function of [tex]g[/tex] of [tex]f(1)[/tex]Firstly, we fill find the composition function [tex](g\°f)(x)[/tex]⇒ [tex](g\°f)(x)=g(f(x))[/tex] [Plugging in [tex]f(x)[/tex] for [tex]x[/tex] ]⇒ [tex]f(x)^2[/tex] ⇒ [tex](7x-3)^2[/tex] [Substituting [tex]f(x)=7x-3[/tex] ] ⇒ [tex]49x^2-42x+9[/tex] [As expansion of [tex](a-b)^2=a^2-2ab+b^2[/tex] ]We can now plugin [tex]x=1[/tex] in the composition function. [tex](g\°f)(1)[/tex]⇒ [tex]49(1)^2-42(1)+9[/tex]⇒ [tex]49-42+9[/tex]⇒ 16∴ [tex](g\°f)(1)=16[/tex]