Verify that the function f and g, are inverses of each other by showing that f(g(x))=x and g(f(x))=x. Graph both the functions on the same graph. Please show all of your work.

Question

f(x)=-7/x-4
g(x)=4x-7/x

Answer 1

I'll do f(g(x)) and that will show you how to do g(f(x))

f(x) = -7/(x-4)
so,
f(g) = -7/(g-4)
but, g = (4x-7)/x, so we have

f(g) = -7/[(4x-7)/x - 4]
= -7/(4 - 7/x - 4)
= -7/(-7/x)
= -7 * (x/-7)
= x