Prove that f and G are inverse functions? F (x) = x + 7, G (x) = X-7

Prove that f and G are inverse functions? F (x) = x + 7, G (x) = X-7

（1） The dependent variable of function f (x) is regarded as the independent variable of a new function g (x), and if the independent variable of this function f (x) is regarded as the dependent variable of the new function g (x), the two functions f (x) and G (x) are called reciprocal functions
（2） In this problem, for f (x) = x + 7, that is y = x + 7
It can be written as x = Y-7
In this case, let x = y, y = x, then y = X-7, that is g (x) = X-7

It is known that f (x) and G (x) are inverse functions of each other~
It is known that f (x) and G (x) are inverse functions of each other, and for any real number a and B, f (a + b) = f (a) f (b). Proof: for any real number m and N, G (MN) = g (m) + G (n). Please explain the process,
How to get f ^ - 1 [f (a) f (b)] = AB,

Let g (m) = a, G (n) = B, then G ^ - 1 (a) = f (a) = m, G ^ - 1 (b) = f (b) = n
f[g(m)+g(n)]=f(a+b)=f(a)f(b)=mn
So g (m) + G (n) = f ^ - 1 (MN) = g (MN)
It's over