Question

G(x)= -x-1 h(x)= x^2 - 5 Find (goh)(x) Find (hog)(x)

Answer 1

The first thing that we need to remember to solve this proble is the definition of (goh)(x) and (hog)(x):

`(h\circ g)(x)=h(g(x))`

And:

`(g\circ h)(x)=g(h(x))`

with those definition in mind we can easily calculate the answer:

`(g\circ h)(x)=g(h(x))=g(x^2-5)=-(x^2-5)-1=-x^2+4^{}`

and:

`(h\circ g)(x)=h(g(x))=h(-x-1)=(-x-1)^2-5=x^2+2x-4`