SpoorthiA451623 SpoorthiA451623
  • 03-11-2022
  • Mathematics
contestada

Let f(x)=x2-2 and g(x)=9-X. Perform the composition or operation indicated.(fg)(-7)

Let fxx22 and gx9X Perform the composition or operation indicatedfg7 class=

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HavishF300799 HavishF300799
  • 03-11-2022

Given the functions below

[tex]\begin{gathered} f(x)=x^2-2 \\ g(x)=9-x \end{gathered}[/tex]

We are to find (fg)(-x)

SOLUTION

First of all, we have to get (fg)(x)

[tex](fg)(x)=(x^2-2)(9-x)[/tex]

Expand the function

[tex]\begin{gathered} (fg)(x)=x^2(9-x)-2(9-x) \\ (fg)(x)=9x^2-x^3-18+2x \\ \therefore(fg)(x)=-x^3+9x^2+2x-18 \end{gathered}[/tex]

Let us now solve for (fg)(-7)

[tex]\begin{gathered} (fg)(-7)=-(-7)^3+9(-7)^2+2(-7)-18 \\ (fg)(-7)=343+441-14-18=752 \end{gathered}[/tex]

Hence,

[tex](fg)(-7)=752[/tex]

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