Suppose that the functions u and w are defined as follows.U(x) = x² +3w (x) = sqrt of x+2Find the following(u • w)(2)=(w • u) (2)=

Answer(there are assumptions for this answer that you need to confirm and look at):Assumptions: [tex]u(x)=x^2+3[/tex] and [tex]w(x)=\sqrt{x+2}[/tex]Answer if the operation is multiplication:If you meant a closed dot which is the symbol for multiplication.[tex](u \cdot w)(2)=14[/tex][tex](w \cdot u)(2)=14[/tex]Answer if the operation is composition:If you meant an open dot which is the symbol for composition.[tex](u \circ w)(2)=7[/tex][tex](w \circ u)(2)=3[/tex]Note: I don't know if you actually meant [tex]w(x)=\sqrt{x+2}[/tex] or if [tex]w(x)=\sqrt{x}+2[/tex]. Please let me know one way or the other.Step-by-step explanation:If we assume the functions are:[tex]u(x)=x^2+3[/tex][tex]w(x)=\sqrt{x+2}[/tex][tex]u \cdot w=w \cdot u[/tex] since multiplication is commutative. [tex]u(2)=2^2+3[/tex][tex]u(2)=4+3[/tex][tex]u(2)=7[/tex][tex]w(2)=\sqrt{2+2}[/tex][tex]w(2)=\sqrt{4}[/tex][tex]w(2)=2[/tex]We are asked to find [tex](u \cdot w)(2)[/tex] and [tex](w \cdot u)(2)[/tex].The order doesn't matter in multiplication.[tex](u \cdot w)(2)[/tex][tex]u(2) \cdot w(2)[/tex][tex]7 \cdot 2[/tex][tex]14[/tex][tex](w \cdot u)(2)[/tex][tex]w(2) \cdot u(2)[/tex][tex]2 \cdot 7[/tex][tex]14[/tex]Now you might have meant composition which symbolized with an open circle, not a closed one.[tex](u \circ w)(2)[/tex][tex]u(w(2))[/tex][tex]u(2)[/tex] since [tex]w(2)=2[/tex][tex]2^2+3[/tex][tex]4+3[/tex][tex]7[/tex][tex](w \circ u)(2)[/tex][tex]w(u(2))[/tex][tex]w(7)[/tex] since [tex]u(2)=7[/tex][tex]\sqrt{7+2}[/tex][tex]\sqrt{9}[/tex][tex]3[/tex]