Given,
The expression of the function,
[tex]\begin{gathered} f(x)=x-3 \\ g(x)=2x^2-x+1 \end{gathered}[/tex]
Required
The value of (fg)(x), (fg)(-2), and (fg)(3).
The value of function (fg)(x),
[tex]\begin{gathered} (fg)(x)=f(x)\times g(x) \\ =(x-3)\times(2x^2-x+1) \\ =2x^3-x^2+x-6x^2+6x-3 \\ =2x^3-7x^2+7x-3 \end{gathered}[/tex]
The value of (fg)(-2),
[tex]\begin{gathered} (fg)(-2)=2x^3-7x^2+7x-3 \\ =2(-2)^3-7(-2)^2+7\times-2-3 \\ =2\times8-7\times4-14-3 \\ =16-28-14-3 \\ =-29 \end{gathered}[/tex]
The value of (fg)(3),
[tex]\begin{gathered} (fg)(3)=2x^3-7x^2+7x-3 \\ =2(3)^3-7(3)^2+7\times3-3 \\ =2\times8-7\times9+21-3 \\ =16-63+21-3 \\ =-29 \end{gathered}[/tex]
Hence, the value of (fg)(3) is -29.
