Question

What is the value of (gof)(4)?

f(x)=4x-7; g(x)=x+3

What is the domain of (fog)(x)?
f(x)=2/x; g(x)=|x|-1

Answer 1

(gof)(x)=g(f(x))
(gof)(4)=g(f(4))

g(f(4))
find f(4) first
f(4)=4(4)-7=16-7=9

g(f(4))=g(9)=9+3=12

(gof)(4)=12




the domain is the usable numbers
(fog)(x)
look at each
f(x)=2/x
x can be any number except 0
find what x in g(x) results in 0
0=|x|-1
add 1
1=|x|
1=x
-1=x

domain of (fog)(x) is all real numbers except for x=-1 and 1

Answer 2

I hope this helps you