Question

Given that f(x)= x2+3 and g(x)= x+4/3 solve for (f(g(x)) when x =2

Answer 1

$\bf \begin{cases} f(x)=x^2+3\\\\ g(x)=x+\cfrac{4}{3} \end{cases} \\\\\\ \boxed{x=2}\qquad g(2)=(2)+\cfrac{4}{3}\implies \boxed{g(2)=\cfrac{10}{3}} \\\\\\ f(~~g(x)~~)=[g(x)]^2+3\implies f(~~g(2)~~)=[g(2)]^2+3 \\\\\\ f(~~g(2)~~)=\left[ \boxed{\frac{10}{3}} \right]^2+3\implies f(~~g(2)~~)=\cfrac{10^2}{3^2}+3 \\\\\\ f(~~g(2)~~)=\cfrac{100}{9}+3\implies f(~~g(2)~~)=\cfrac{100+27}{9} \\\\\\ f(~~g(2)~~)=\cfrac{127}{9}$