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]
