Question

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

Answer 1

Answer and explanation:

Given : $f(x)=y=\frac{3x}{8+x}$

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,

$x=\frac{3y}{8+y}$

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,

$y=\frac{8x}{3-x}$

or $y=f^{-1}(x)=\frac{8x}{3-x}$

Answer 2

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) ....