Respuesta :
Given the functions:
[tex]\begin{gathered} f\mleft(x\mright)=x^2-2 \\ \\ g\mleft(x\mright)=x^3+2 \end{gathered}[/tex]You need to multiply them in order to find:
[tex](f\cdot g)(x)[/tex]Then, you get:
[tex](f\cdot g)(x)=\mleft(x^2-2\mright)\mleft(x^3+2\mright)[/tex][tex](f\cdot g)(x)=(x^2)(x^3)+(x^2)(2)-(2)(x^3)-(2)(2)^{}[/tex][tex](f\cdot g)(x)=x^5+2x^2-2x^3-4[/tex][tex](f\cdot g)(x)=x^5-2x^3+2x^2-4[/tex]Substitute the following value of "x" into the function:
[tex]x=-2[/tex]And then evaluate, in order to find:
[tex]\mleft(f\cdot g\mright)\mleft(-2\mright)[/tex]Then, you get:
[tex](f\cdot g)(-2)=(-2)^5-2(-2)^3+2(-2)^2-4[/tex][tex]\begin{gathered} (f\cdot g)(-2)=(-2)^5-2(-2)^3+2(-2)^2-4 \\ \\ (f\cdot g)(-2)=-32-2(-8)^{}+2(4)^{}-4 \end{gathered}[/tex][tex](f\cdot g)(-2)=-32+16^{}+8^{}-4[/tex][tex](f\cdot g)(-2)=-12[/tex]Hence, the answer is:
[tex](f\cdot g)(-2)=-12[/tex]