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.
