Answer:
Option (2)
Step-by-step explanation:
If m(x) and n(x) are the functions inverse of each other,
Then the following condition should be fulfilled,
m[n(x)] = n[m(x)] = x
Here, m(x) = [tex]\frac{3x}{x+7}[/tex] and n(x) = [tex]\frac{7x}{3-x}[/tex]
m[n(x)] = [tex]\frac{3(\frac{7x}{3-x})}{(\frac{7x}{3-x})+7}[/tex]
= [tex]\frac{21x}{7x+21-7x}[/tex]
= x
n[m(x)] = [tex]\frac{7(\frac{3x}{x+7})}{3-\frac{3x}{x+7}}[/tex]
= [tex]\frac{21x}{3x+21-3x}[/tex]
= x
Therefore, [tex]\frac{3(\frac{7x}{3-x})}{(\frac{7x}{3-x})+7}=\frac{7(\frac{3x}{x+7})}{3-\frac{3x}{x+7}}=x[/tex] will be the correct option.
Option (2) will be the answer.
