Question

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.

Answer 1

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 2

Answer and explanation:

Given :
`f(x)=y=(3x)/(8+x)`

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,

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

Step 2 - Cross multiply,

`x(8+y)=3y`

Step 3 - Apply distributive property,

`8x+xy=3y`

Step 4 - Take y term one side,

`8x=3y-xy`

Step - 5 Take y common,

`8x=y(3-x)`

Step 6 - Take x term together,

`y=(8x)/(3-x)`

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