Respuesta :
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]