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

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Answer 1 · 2018-04-16T15:34:47

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

$(g @ f)(x)=g(f(x))$

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

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

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

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

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