SOLUTION: I really need help on this. It would be immensely awesome if you would offer some guidance: Let f(x)=(6 - x)/(3 + 4x) (a) Find f^-1 , the inverse function of f. S

Algebra ->  Functions -> SOLUTION: I really need help on this. It would be immensely awesome if you would offer some guidance: Let f(x)=(6 - x)/(3 + 4x) (a) Find f^-1 , the inverse function of f. S      Log On


   



Question 1039858: I really need help on this. It would be immensely awesome if you would offer some guidance:
Let f(x)=(6 - x)/(3 + 4x)
(a) Find f^-1 , the inverse function of f. Show work.





(b) What is the domain of f ? What is the domain of the inverse function?



(c) What is f (3) ? f (3) = ______



(d) What is f^-1 ( ____ ), where the number in the blank is your answer from part (c)?

Any help on this is extremely helpful, thank you so much!

Answer by Aldorozos(172) About Me  (Show Source):
You can put this solution on YOUR website!
Y=(6-x)/(3+4x)
Y(4+4x)=6-x
X(4y+1)=6-36
X=6-3y/(4y+1)
Replacing x with y
Y=6-3x/(4x-1) which is the inverse
Domain of f, can be any number R except x= -3/4
Since the denominator of f can't be zero
3+4x can't be zero
Similarly the denominator of inverse function can't be zero
Therefore for invers x can't be 1/4
If x= 3 f would be 1/5
What is inverse if we replace x in inverse with 1/5
6-3(1/5) divided by 4(1/5)-1