Question 1133183

Provided 

{{{f(x) = sqrt(x+2) }}}

{{{g(x) = x / (x + 1 )}}}


Find ({{{f}}} ◦ {{{g}}})({{{3}}}) and ({{{g}}} ◦ {{{f}}})({{{3}}}). 


first find

({{{f}}} ◦ {{{g}}})({{{x}}}) ={{{f(g(x))}}}

({{{f}}} ◦ {{{g}}})({{{x}}}) ={{{f(x / (x + 1 ))}}}

({{{f}}} ◦ {{{g}}})({{{x}}}) ={{{sqrt(x / (x + 1 )+2)}}}

({{{f}}} ◦ {{{g}}})({{{x}}}) ={{{sqrt(x / (x + 1 )+2(x + 1 )/(x + 1 ))}}}

({{{f}}} ◦ {{{g}}})({{{x}}}) ={{{sqrt((x +2(x + 1 ))/(x + 1 ))}}}

({{{f}}} ◦ {{{g}}})({{{x}}}) ={{{sqrt((x +2x + 2 ))/(x + 1 ))}}}

({{{f}}} ◦ {{{g}}})({{{x}}}) ={{{sqrt((3x + 2 ))/(x + 1 ))}}}

=>
({{{f}}} ◦ {{{g}}})({{{3}}}) ={{{sqrt((3*3 + 2 )/(3 + 1 ))}}}

({{{f}}} ◦ {{{g}}})({{{3}}}) ={{{sqrt(11/4)}}}

({{{f}}} ◦ {{{g}}})({{{3}}}) ={{{sqrt(11)/2}}}

({{{f}}} ◦ {{{g}}})({{{3}}}) ={{{1.658}}}



({{{g}}} ◦ {{{f}}})({{{x}}}) ={{{g(f(x))}}}

({{{g}}} ◦ {{{f}}})({{{x}}}) ={{{g(sqrt(x+2))}}}

({{{g}}} ◦ {{{f}}})({{{x}}}) ={{{sqrt(x+2) / (sqrt(x+2) + 1 )}}}


=>
({{{g}}} ◦ {{{f}}})({{{3}}}) ={{{sqrt(3+2) / (sqrt(3+2) + 1 )}}}

({{{g}}} ◦ {{{f}}})({{{3}}}) ={{{sqrt(5) / (sqrt(5) + 1 )}}}

({{{g}}} ◦ {{{f}}})({{{3}}}) ={{{0.69}}}