SOLUTION: Hello, quick question. I need to find the inverse of this function. And the domain and range of it. f(x)= 3/x-7 This is the answer that I got, did I do anything wrong? Doma

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hello, quick question. I need to find the inverse of this function. And the domain and range of it. f(x)= 3/x-7 This is the answer that I got, did I do anything wrong? Doma      Log On


   

Question 462903: Hello, quick question. I need to find the inverse of this function. And the domain and range of it.
f(x)= 3/x-7
This is the answer that I got, did I do anything wrong?
Domain of f: (-infinity, 7)U(7, infinity)
Range of f: (-infinity, 0)U(0, infinity)
f-1(x)= (3/x)+7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If the function is f%28x%29=3%2F%28x-7%29, then replace f(x) with y, then swap x and y to get x=3%2F%28y-7%29 and solve for y


x=3%2F%28y-7%29


x%28y-7%29=3


y-7=3%2Fx


y=3%2Fx%2B7


So the inverse function is


Domain of f: (ie you can plug in any number but 7 since this value results in a division by zero)



Range of f: (this is equal to the horizontal asymptote)


Now simply flip the domain and range of f(x) to get the domain and range for the inverse



Domain of :



Range of :