Question

F(x) = 2x + 3g(x) = 2x² + 6x + 13Find: (gºf)(x)

Answer 1

The function (gof)(x) is;

`(g\circ f)(x)=8x^2+36x+49`

Step-by-step explanation:

Given the functions;

`\begin{gathered} f(x)=2x+3 \\ g(x)=2x^2+6x+13 \end{gathered}`

Solving for the function;

`(g\circ f)(x)=g(f(x))`

so, we have;

`\begin{gathered} g(f(x))=2(f(x))^2+6(f(x))+13 \\ g(f(x))=2(2x+3)^2+6(2x+3)+13 \\ g(f(x))=2(4x^2+12x+9)^{}+6(2x)+6(3)+13 \\ g(f(x))=8x^2+24x+18^{}+12x+18+13 \\ g(f(x))=8x^2+24x^{}+12x+18+18+13 \\ g(f(x))=8x^2+36x+49 \end{gathered}`

Therefore, the function (gof)(x) is;

`(g\circ f)(x)=8x^2+36x+49`