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

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) (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
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