Answer:
[tex]f(x)\cdot g(x)=x^3-2x^2-x+2[/tex]
Explanation:
Given f(x) and g(x) defined below:
[tex]\begin{gathered} f(x)=x^2-1 \\ g(x)=x-2 \end{gathered}[/tex]
The combination of f(x) and g(x) is obtained below:
[tex]f(x)\cdot g(x)=\lbrack x^2-1\rbrack\lbrack x-2\rbrack[/tex]
Next, expand the brackets and simplify:
[tex]\begin{gathered} =x^2\lbrack x-2\rbrack-1\lbrack x-2\rbrack \\ =x^3-2x^2-x+2 \\ \implies f(x)\cdot g(x)=x^3-2x^2-x+2 \end{gathered}[/tex]
