Question

F(x) = x 4x + 6g(x) = 3.x = 1Find: (gºf)(x)

Answer 1

Consider the given functions,

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

Solve for the composite function as follows,

`\begin{gathered} g\circ f(x) \\ =g\mleft(f\mleft(x\mright)\mright) \\ =g\mleft(x^2-4x+6\mright) \\ =-3(x^2-4x+6)+1 \\ =-3x^2+12x-18+1 \\ =-3x^2+12x-17 \end{gathered}`

Thus, the required composit function is obtained as,

`g\circ f(x)=-3x^2+12x-17`