Question

How do you find (g o f)(x) when `f(x)=2x` and `g(x)=x^3+x^2+1`?

Answer 1

`color(blue)(8x^3+4x^2+1)`

Explanation:

`(g @ f)(x)=g(f(x))`

To find the result we substitute `x=f(x)` in `g(x)`:

`g(x)=x^3+x^2+1`

`g(f(x))=(f(x))^3+(f(x))^2+1=(2x)^3+(2x)^2+1`

`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =8x^3+4x^2+1`