Verify that the functions f and g, are inverses of each other by showing that f(g(x))=x and g(f(x))=x. f(x)=-7/x-4 g(x)=4x-7/xPLEASE SHOW ALL WORK!!!!!
You need to remember how the composition of two function works, hence `f(g(x)) = (fog)(x).`
Substituting g(x) for x in the equation of f(x) yields:
`f(g(x)) = f((4x-7)/x) = -7/((4x-7)/x - 4)`
You need to bring the terms `(4x-7)/x` and 4 to a common denominator such that:
`(4x-7)/x - 4 = (4x - 7 - 4x)/x = (-7)/x`
Hence `f(g(x)) = -7/(-7/x)`
You need to multiply -7 by the reversed denominator such that:
`f(g(x)) = -7*(-x/7) =` x
You need to prove that g(f(x)) = x, hence, substituting `-7/(x-4)` for f(x) in the equation of g(x) yields:
`g(f(x)) = g(-7/(x-4)) = (4(-7/(x-4)) - 7)/x`
`` `g(f(x)) = (-28 - 7x + 28)/x(x-4) = -7/(x-4) = f(x)`
Hence, since g(f(x)) yields f(x), the functions f(x) and g(x) are not inverse to each other.