Question 1138461

given:
 
{{{f(x) = (x^2 + 3x + 1)}}}, 
{{{g(x) = (3x + 1)}}} and 
{{{h(x) = 3x + (2/x)}}}


Find 

({{{f}}}o{{{g}}}o{{{h}}})({{{x}}})


({{{f}}}o{{{g}}}o{{{h}}})({{{x}}})={{{f(g(h(x)))}}}


first find {{{g(h(x))}}}

{{{g(h(x))=g(3x + (2/x))}}}
{{{g(h(x))=3(3x + (2/x)) + 1)}}}
{{{g(h(x))=9x + 6/x + 1}}}


now find

{{{f(9x + 6/x + 1)=(9x + 6/x + 1)^2 + 3(9x + 6/x + 1) + 1}}}

{{{f(9x + 6/x + 1)=(9 x^2 + x + 6)^2/x^2 + (27 x^2 + 3 x + 18)/x + 1}}}

{{{f(9x + 6/x + 1)=(9 x^2 + x + 6)^2/x^2 + x(27 x^2 + 3 x + 18)/x^2 + x^2/x^2}}}

{{{f(9x + 6/x + 1)=((9 x^2 + x + 6)^2 + x(27x^2 + 3 x + 18) + x^2)/x^2}}}

{{{f(9x + 6/x + 1)=(81 x^4 + 45 x^3 + 113 x^2 + 30x + 36)/x^2}}}

{{{f(9x + 6/x + 1)=81 x^2 + (30x + 36)/x^2 + 45x + 113}}}

{{{f(9x + 6/x + 1)=81 x^2 + 6(5x + 6)/x^2 + 45x + 113}}}


=>{{{f(g(h(x)))=81 x^2 + 6(5x + 6)/x^2 + 45x + 113}}}