The functions m(x) and n(x) are inverses of each other and this is shown by the equation in option B.
What is an Inverse Function?
To find an inverse function of a function (x,y), the y and x are interchanged and the equation is then solved for y.
The functions are :
[tex]\rm m(x) = \dfrac{3x}{x+7}[/tex]
[tex]\rm n(x) = \dfrac{7x}{3-x}[/tex]
The inverse of the function m(x) will be determined to check if both the functions given are inverse of each other
Let m(x) = y
[tex]\rm y= \dfrac{3x}{x+7}\\\\\\On \; Interchanging \ ; x \;a nd\; y\\\\x = \dfrac{3y}{y+7}[/tex]
As n(x) is the inverse of m(x) ,
[tex]\rm y = n(x) = \dfrac{7x}{3-x}[/tex]
Equation 1 is
[tex]\rm x = \dfrac{3( \dfrac{7x}{3-x})}{\dfrac{7x}{3-x} +7}\\[/tex]
same goes for function n(x)
[tex]\rm x = \dfrac{7y}{3-y}\\\\\\Equation \; 2 \; is\\x = \dfrac{7( \dfrac{3x}{x+7})}{3 - (\dfrac{3x}{x+7})}[/tex]
From equation 1 and 2
[tex]\rm x = \dfrac{3( \dfrac{7x}{3-x})}{\dfrac{7x}{3-x} +7} = \dfrac{7( \dfrac{3x}{x+7})}{3 - (\dfrac{3x}{x+7})}[/tex]
Therefore, the correct option is B
To know more about Inverse Function
https://brainly.com/question/2541698
#SPJ2
