Answer:
98
Step-by-step explanation:
So we have the two functions:
[tex]g(x)=-2x-2\text{ and } r(x)=x^2-2[/tex]
And we want to find the value of r(g(4)).
To do so, first find the value of g(4):
[tex]g(x)=-2x-2\\g(4)=-2(4)-2\\[/tex]
Multiply:
[tex]g(4)=(-8)-2[/tex]
Subtract:
[tex]g(4)=-10[/tex]
Now, substitute this into r(g(4)):
[tex]r(g(4))\\=r(-10)[/tex]
And substitute this value into r(x):
[tex]r(-10)=(-10)^2-2[/tex]
Square:
[tex]r(-10)=100-2[/tex]
Subtract:
[tex]r(-10)=98[/tex]
Therefore:
[tex]r(-10)=r(g(4))=98[/tex]
