Prove that f(x)=2x+4 and g(x)=x-4/2 are inverses of each other. show your work.

If f(x) is the inverse of g(x), then f(g(x))=f(g(x))=x
or we can do it the hard way and solve for the inverses (I'm too lazy to do that)

I'm assuming you means g(x)=(x-4)/2

so
show that f(g(x))=g(f(x))=x
first do f(g(x))

f(g(x))=2((x-4)/2)+4
f(g(x))=x-4+4
f(g(x))=x

g(f(x))=(2x+4-4)/2
g(f(x))=(2x)/2
g(f(x))=x

both equal x and x=x so f(g(x))=f(g(x))=x

they are iinverses
if you did want to solve then
do, f(x)=y, then swtich all x and y then solve for x
example
f(x)=2x+4 then y=2x+4 then x=2y+4 then x-4=2y then (x-4)/2=y=g(x)
then reverse it to get the other inverse thing