Question

If f(x)=-x^2-1 and g(x)=x+5 then f(g(x)) =

Answer 1

The composition of f(g(x)) is:

`f(g(x)) = -x^2-10x-26`

Explanation:

Given two functions are:

`f(x) = -x^2-1\\g(x) = x+5`

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

`f(g(x)) = -(x+5)^2-1\\=-(x^2+25+10x)-1\\=-x^2-25-10x-1\\=-x^2-10x-26`

Hence,

The composition of f(g(x)) is:

`f(g(x)) = -x^2-10x-26`