Question

solve the functionf(x)=x^3-4x^2+x+1g(x)=x^2-6solve for f(g(3))

Answer 1

Given:

$\begin{gathered} f\mleft(x\mright)=x^3-4x^2+x+1 \\ g\mleft(x\mright)=x^2-6 \end{gathered}$

To find the composition function,

$\begin{gathered} (f\circ g)(x)=f(g(x)) \\ =f(x^2-6) \\ =(x^2-6)^3-4(x^2-6)^2+(x^2-6)+1 \\ \Rightarrow f(g(x))=(x^2-6)^3-4(x^2-6)^2+(x^2-6)+1 \\ f(g(3))=(x^2-6)^3-4(x^2-6)^2+(x^2-6)+1 \\ =(3^2-6)^3-4(3^2-6)^2+(3^2-6)+1 \\ =27-36+3+1 \\ =-5 \end{gathered}$

Answer: f(g(3)) = -5