Consider the function...

Question

 Consider the function  for f(x) = 9/(x-6) for x > 6.

(A) Find f^-1(7) = ?

(B) Use Theorem 7, page 156 of the Stewart Essential Calculus textbook to find (f^-1)(7) (f^-1)(7) = ?

 (C) Calculate  and state domain and range of .Use interval notation. If needed enter inf for  or -inf

f^-1(x) = ?

 for . 

Domain = ?

Range = ?

Calculate (f^-1)(7) from the formula for f^-1(x) and check that it agrees with the result of part (B)

Answer 1

I will only give you a hint for this problem because I think you have probably not submitted it entirely and/or correctly.

If f(x)=9/(x-6), write this as y=9/(x-6).

Interchange the roles of x and y:

x=9/(y-6)

solve for y

y=6+(9/x)

and f^-1(x)=6+(9/x)

You will probably also want to know about derivatives...and I will leave that to you.