The given functions are
[tex]l(x)=|x|[/tex][tex]m(x)=-x^2[/tex]
The composition function can be written as follows:
[tex]l(m(x)=l(-x^2)[/tex]
[tex]=|-x^2|[/tex][tex]We\text{ know that }-x^2\text{ always negative for all values of x}[/tex][tex]|-x^2|=x^2[/tex]
Therefore the algebraic expression of composition is
[tex]l(m(x)=x^2[/tex]
The table values are
[tex]x=-3,\text{ composition=}(-3)^2=9[/tex]
[tex]x=-2,\text{ composition=}(-2)^2=4[/tex]
[tex]x=-1,\text{ composition=}(-1)^2=1[/tex]
[tex]x=0,\text{ composition=}(0)^2=0[/tex]
[tex]x=1,\text{ composition=}(1)^2=1[/tex]
[tex]x=2,\text{ composition=}(2)^2=4[/tex]
[tex]x=3,\text{ composition=}(3)^2=9[/tex]
