Let a(x) and b(x) be functions. Find (a\circ b)(3) - (b\circ a)(3) if $a(x) = 2x + 5$ and $b(x) = 4 - x^2$.

To find ((a \circ b)(3) - (b \circ a)(3)), we first need to compute ((a \circ b)(3)) and ((b \circ a)(3)).

1. Calculate ( (a \circ b)(3) ): The composition ( (a \circ b)(x) ) is defined as ( a(b(x)) ). We start by finding ( b(3) ): [ b(x) = 4 - x^2 ] Therefore, [ b(3) = 4 - 3^2 = 4 - 9 = -5 ]

   Now, we need to evaluate ( a(b(3)) = a(-5) ): [ a(x) = 2x + 5 ] Thus, [ a(-5) = 2(-5) + 5 = -10 + 5 = -5 ]

   Therefore, ( (a \circ b)(3) = -5 ).

2. Calculate ( (b \circ a)(3) ): The composition ( (b \circ a)(x) ) is defined as ( b(a(x)) ). First, we find ( a(3) ): [ a(3) = 2(3) + 5 = 6 + 5 = 11 ]

   Now, we need to evaluate ( b(a(3)) = b(11) ): [ b(11) = 4 - 11^2 = 4 - 121 = -117 ]

   Thus, ( (b \circ a)(3) = -117 ).

3. Combine results: We now have: [ (a \circ b)(3) = -5 ] [ (b \circ a)(3) = -117 ]

Now we find ( (a \circ b)(3) - (b \circ a)(3) ): [ (a \circ b)(3) - (b \circ a)(3) = -5 - (-117) = -5 + 117 = 112 ]

Thus, the final result is: [ \boxed{112} ]