Is f(x)=3x-1 and g(x)=(x+1)/3 inverses of each other?

Answer 1

If the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, i.e., g(y) = x if and only if f(x) = y

Given f(x) = 3x -1, Let f(x) = y = 3x-1

Given g(x) = (x+1)/3 , so that g(y) = (y+1)/3

g(f(x))=g(y)=[(3x-1)+1]/3=x

vise versa,

Let g(x)=(x+1)/3

f(g(x))=3*g(x)-1=3((x+1)/3)-1=x

So f(x) and g(x) are inverse of each other.