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

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Answer 1 · 2017-09-11T05:01:48

$f (g (x)) = x^{2}$ $f(g(x))=x^2$ and and $g (g (x)) = x^{4}$ $g(g(x))=x^4$

As $f (x) = | x |$ $f(x)=|x|$ and $g (x) = x^{2}$ $g(x)=x^2$

$f (g (x)) = | g (x) | = ∣ ∣ x^{2} ∣ ∣ = x^{2}$ $f(g(x))=|g(x)|=|x^2|=x^2$

and $g (g (x)) = {(g (x))}^{2} = {(x^{2})}^{2} = x^{4}$ $g(g(x))=(g(x))^2=(x^2)^2=x^4$

How do you determine f(g(x))f(g(x))f(g(x)) and g(g(x))g(g(x))g(g(x)), given f(x)=absxf(x)=|x|f(x)=absx and g(x)=x^2g(x)=x2g(x)=x^2?