Answer:
Step-by-step explanation:
A). If a function 'f' is inverse of another function 'g',
Then f[g(x)] = x = g[f(x)]
In this question the given functions are,
f(x) = [tex]\frac{1}{x-3}[/tex] and g(x) = [tex]\frac{3x+1}{x}[/tex]
Then, f[g(x)] = [tex]\frac{1}{\frac{3x+1}{x}-3}[/tex]
= [tex]\frac{x}{3x+1-3x}[/tex]
= x
Similarly, g[f(x)] = [tex]\frac{(\frac{3}{x-3})+1}{\frac{1}{x-3} }[/tex]
= [tex]\frac{3+x-3}{1}[/tex]
= x
Therefore, Both the functions are inverse of each other.
B). Domain of the compositions of these functions will be a set of all real numbers, (-∞, ∞)
