Respuesta :

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.

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