1 Answer

Hubris · Answer 1 · 2023-02-15T15:47:38+0000

Given,

The expression of the function,

$\begin{gathered} f(x)=x-3 \\ g(x)=2x^2-x+1 \end{gathered}$

Required

The value of (fg)(x), (fg)(-2), and (fg)(3).

The value of function (fg)(x),

$\begin{gathered} (fg)(x)=f(x)* g(x) \\ =(x-3)*(2x^2-x+1) \\ =2x^3-x^2+x-6x^2+6x-3 \\ =2x^3-7x^2+7x-3 \end{gathered}$

The value of (fg)(-2),

$\begin{gathered} (fg)(-2)=2x^3-7x^2+7x-3 \\ =2(-2)^3-7(-2)^2+7*-2-3 \\ =2*8-7*4-14-3 \\ =16-28-14-3 \\ =-29 \end{gathered}$

The value of (fg)(3),

$\begin{gathered} (fg)(3)=2x^3-7x^2+7x-3 \\ =2(3)^3-7(3)^2+7*3-3 \\ =2*8-7*9+21-3 \\ =16-63+21-3 \\ =-29 \end{gathered}$

Hence, the value of (fg)(3) is -29.

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