Question

sendo f(x)=1-4x e g(x)=x²+x-1 determine

g0f(1)​

Answer 1

$\Large\boxed{\begin{array}{l}\sf f(x)=1-4x\\\sf g(x)=x^2+x-1\\\sf g\circ f(x)=g[f(x)]\\\sf g[f(x)]=f(x)^2+f(x)-1\\\sf g[f(x)]=(1-4x)^2+(1-4x)-1\\\sf g[f(x)]=1-8x+16x^2+\backslash\!\!\!1-4x-\backslash\!\!\!1\\\sf g[f(x)]=16x^2-12x+1\\\sf g[f(1)]=16\cdot1^2-12\cdot1+1\\\sf g[f(1)]=16-12+1\\\sf g[f(1)]=5\end{array}}$