Explicación paso a paso:
[tex]f(x) = {x}^{2} \: \: y \: \: \: g(x) = \frac{1}{ {x}^{3} } \\ fof = f(f(x)) = f( {x}^{2} ) = {( {x}^{2} )}^{2} = {x}^{4} \\ gog = g(g(x)) = g( \frac{1}{x} ) = \frac{1}{ \frac{1}{ {x}^{3} } } = {x}^{3} \\ f(g(x)) = f( \frac{1}{ {x}^{3} } ) = ( { \frac{1}{ {x}^{3} } })^{2} = \frac{1}{ {x}^{6} } \\ gof = g(f(x)) = g( {x}^{2} ) = \frac{1}{ ({ {x}^{2} )}^{3} } \\ g(f(x)) = \frac{1}{ {x}^{6} } [/tex]
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Verified answer
Explicación paso a paso:
[tex]f(x) = {x}^{2} \: \: y \: \: \: g(x) = \frac{1}{ {x}^{3} } \\ fof = f(f(x)) = f( {x}^{2} ) = {( {x}^{2} )}^{2} = {x}^{4} \\ gog = g(g(x)) = g( \frac{1}{x} ) = \frac{1}{ \frac{1}{ {x}^{3} } } = {x}^{3} \\ f(g(x)) = f( \frac{1}{ {x}^{3} } ) = ( { \frac{1}{ {x}^{3} } })^{2} = \frac{1}{ {x}^{6} } \\ gof = g(f(x)) = g( {x}^{2} ) = \frac{1}{ ({ {x}^{2} )}^{3} } \\ g(f(x)) = \frac{1}{ {x}^{6} } [/tex]