Question

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

Answer 1

Answer:

Step-by-step explanation:

f(x) = y = 3x/(8 + x)   (I am assuming that the 8 + x is the denominator. Please use parentheses in the future if you forgot this. If there are no parentheses, then my solution will not work for you.)

 

Exchange x and y; that is, replace x by y and y by x simultaneously:

 

x = 3y/(8 + y).

 

Then use algebra to solve for y in terms of x:

 

(8 + y)x = 3y    (multiply both sides by the denominator to clear the fraction)

8x + xy = 3y     (distribute)

xy − 3y = −8x     (rearrange terms with all y's on the left side of the equation)

y(x − 3) = −8x    (factor out y as a common factor)

y = −8x/(x − 3)    (divide by x − 3)

 

Finally, replace y by f-1(x):

 

f-1(x) = −8x/(x − 3).

 

This is the inverse of f(x). It can be checked by finding f(f-1(x)) and f-1(f(x)), and verifying that both equal x after simplifying.