How do you determine $f (g (x))$ $f(g(x))$ and $g (g (x))$ $g(g(x))$ , given $f (x) = x^{2} + x$ $f(x)=x^2+x$ and $g (x) = x^{2} + x$ $g(x)=x^2+x$ ?

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Answer 1 · 2017-02-26T07:19:26

The answers are $f (g (x)) = g (g (x)) = (x^{2} + x) (x^{2} + x + 1)$ $f(g(x))=g(g(x))=(x^2+x)(x^2+x+1)$

This is a compositio of functions

$f (x) = x^{2} + x$ $f(x)=x^2+x$

$g (x) = x^{2} + x$ $g(x)=x^2+x$

$f (g (x)) = f (x^{2} + x) = {(x^{2} + x)}^{2} + (x^{2} + x)$ $f(g(x))=f(x^2+x)=(x^2+x)^2+(x^2+x)$

$= (x^{2} + x) (x^{2} + x + 1)$ $=(x^2+x)(x^2+x+1)$

$g (g (x)) = g (x^{2} + x) = {(x^{2} + x)}^{2} + (x^{2} + x)$ $g(g(x))=g(x^2+x)=(x^2+x)^2+(x^2+x)$

$= (x^{2} + x) (x^{2} + x + 1)$ $=(x^2+x)(x^2+x+1)$

How do you determine f(g(x))f(g(x)) and g(g(x))g(g(x)), given f(x)=x2+xf(x)=x^2+x and g(x)=x2+xg(x)=x^2+x?