Question 1162538
{{{f(x) = x + 2 }}}and 
{{{g(x) = 3^x}}} 

determine an equation for: 

a.

({{{f}}} ∘ {{{g}}})({{{x}}}) ={{{f(g(x))=f(3^x)=3^x+2}}}

and 
({{{g }}}∘ {{{f}}})({{{x}}})={{{g(f(x))=g(x+2)=3^(x+2)}}}

b. Determine {{{f(g(3))}}} and {{{g(f(3))}}}. 

first {{{g(3) = 3^3=27}}}

{{{f(g(3))=x+2=27+2=29}}}


{{{f(3) = x + 2=3+2=5 }}}

{{{g(f(3))=3^x=3^5=243}}}




c) Determine all values of {{{x}}} for which {{{f(g(x)) = g(f(x))}}}.

{{{x+2=3^x}}}....evidently, one solution is {{{x=1}}}

verify:


{{{1+2=3^1}}}
{{{3=3}}}->true