Answer:
The composition of f(g(x)) is:
[tex]f(g(x)) = -x^2-10x-26[/tex]
Step-by-step explanation:
Given two functions are:
[tex]f(x) = -x^2-1\\g(x) = x+5[/tex]
we have to find the composition of f and g which can also be written as: fog(x) or f(g(x))
The method to find the composition is that we will put the function g in place of x in function f
[tex]f(g(x)) = -(x+5)^2-1\\=-(x^2+25+10x)-1\\=-x^2-25-10x-1\\=-x^2-10x-26[/tex]
Hence,
The composition of f(g(x)) is:
[tex]f(g(x)) = -x^2-10x-26[/tex]
