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Drag each tile to the correct box. Not all tiles will be used.

Arrange the equations in the correct sequence to find the inverse of f(x) = y = 3x/8+x.

Drag each tile to the correct box Not all tiles will be used Arrange the equations in the correct sequence to find the inverse of fx y 3x8x class=

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Answer:

Step-by-step explanation:

f(x) = y = 3x/8+x.

Always use parenthesis for denominators which consist of more than a single term.

f(x) = y = 3x/(8+x)

Now switch x and y

x=3y/(8+y)

x(8+y)=3y

Now multiply x by the expression

8x+xy=3y

8x=3y-xy

Now take y as common:

8x= y(3-x)

y=f^-1(x)=8x/(3-x) ....

Answer and explanation:

Given : [tex]f(x)=y=\frac{3x}{8+x}[/tex]

To find : Arrange the equations in the correct sequence to find the inverse of f(x) ?

Solution :

Writing step by step to find inverse,

Step 1 - Interchange y with x,

[tex]x=\frac{3y}{8+y}[/tex]

Step 2 - Cross multiply,

[tex]x(8+y)=3y[/tex]

Step 3 - Apply distributive property,

[tex]8x+xy=3y[/tex]

Step 4 - Take y term one side,

[tex]8x=3y-xy[/tex]

Step - 5 Take y common,

[tex]8x=y(3-x)[/tex]

Step 6 - Take x term together,

[tex]y=\frac{8x}{3-x}[/tex]

or [tex]y=f^{-1}(x)=\frac{8x}{3-x}[/tex]

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