Question 4808
(f o g)(3) given {{{f(x) = 11x + 5}}} and {{{g(x) = x^2 + 8x}}}

(f o g)(3) means f[ g(3) ], so the first order of business is to find g(3).  Go to the g(x) formula and substitute 3 for the x, giving you {{{3^2 + 8* 3}}} 

g(3) = 9 + 24 = 33

Now, find f[ g(3) ] = f[ 33 ] = 11*33 + 5 = 3685  




Second problem (g o f)(2), Given {{{f(x) = 2x + 9 }}}and {{{g(x) = x^2 + 7x}}}

(g o f)(2) means g[ f(2) ], so you first have to find f(2) using the f(x) formula.
f(2) = 2*2 + 9 = 13

Now you have to find g(13) using the g(x) formula:
(g o f)(2) = g[ f(2) ] = g[ 13 ] = {{{13^2 + 7* 13}}} = 169 + 91 = 260


There really isn't a good way to check these without going to twice as much work as solving them to begin with.  Such ugly answers!  Sorry about that.  


R^2 at SCC