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Sagot :
Solution:
Given the functions below
[tex]\begin{gathered} F(x)=6x+4 \\ g(x)=4-x^2 \end{gathered}[/tex]a) For F(g(0))
Firstly, F(g(x) will give
[tex]\begin{gathered} \left(F∘g\right)\left(x\right)=F\mleft(g\mleft(x\mright)\mright)=6(4-x^2)+4=24-6x^2+4=28-6x^2 \\ F(g(x))=28-6x^2 \\ F(g(0))=28-6(0)^2=28-0=28 \\ F(g(x))=28 \end{gathered}[/tex]Hence, F(g(0)) is 28
b) For g(F(0))
Firstly, g(F(x) will give
[tex]\begin{gathered} g\mleft(F(x)\mright)=4-(6x+4)^2=4-36x^2-48x-16=-36x^2-48x-12 \\ g(F(0))=-36(0)^2-48(0)-12=0-0-12=-12 \\ g(F(x))=-12 \end{gathered}[/tex]Hence, g(F(0)) is -12
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