Answer:
The functions are given below as
[tex]f\lparen x)=3x+5,g\lparen x)=2x^2-4x+8[/tex]Concept:
To figure out f(x0.g(x), we will use the formula below
[tex]f\mleft(x\mright).g\mleft(x\mright)=f\mleft(x\mright)\times g\mleft(x\mright)[/tex]By substituting the values, we will have
[tex]f\mleft(x\mright).g\mleft(x\mright)=\left(3x+5\right?\left(2x^2-4x+8\right?[/tex]By expanding the brackets, we will have
[tex]\begin{gathered} f\mleft(x\mright).g\mleft(x\mright)=3x\left(2x^2-4x+8\right?+5\left(2x^2-4x+8\right? \\ f\mleft(x\mright).g\mleft(x\mright)=6x^3-12x^2+24x+10x^2-20x+40 \\ f\mleft(x\mright).g\mleft(x\mright)=6x^3-12x^2+10x^2+24x-20x+40 \\ f\mleft(x\mright).g\mleft(x\mright)=6x^3-2x^2+4x+40 \end{gathered}[/tex]Hence,
The final answer is
[tex]f\mleft(x\mright).g\mleft(x\mright)=6x^3-2x^2+4x+40[/tex]
