Hi all...I'm back.
"Let f(x) = (2x - 3)/(x + 4). Find f^-1(x). Find the domain and range of f(x) and f^-1(x). What do you observe?"
I got all the way down to where it asks "what do you observe" I see what I think I am supposed to see, but I don't know how to put it into words.
f^-1(x) = (-4x - 3)/(x -2)
Domain f(x) = all real numbers except -4
Range f(x) = 3/2
Domain f^-1(x) = all real numbers except 2
Range f^-1(x) = -(3/4)
I see that the numbers in the domain and range in one function are in the equation of the opposite function. Is there a more mathematical way of saying this? Or even a better way?
One more question:
"assume that the domain of f and f^-1 is all real numbers. Solve the equation for x using the given information."
f^-1(2x + 3) = 5 ; f(5) = 13
I'm not sure what they are asking me to do. I know I can't plug the 5 into the inverse function because then I would not be solving for x. How do I get started with this?
Thank you so much.
Jenny
"Let f(x) = (2x - 3)/(x + 4). Find f^-1(x). Find the domain and range of f(x) and f^-1(x). What do you observe?"
I got all the way down to where it asks "what do you observe" I see what I think I am supposed to see, but I don't know how to put it into words.
f^-1(x) = (-4x - 3)/(x -2)
Domain f(x) = all real numbers except -4
Range f(x) = 3/2
Domain f^-1(x) = all real numbers except 2
Range f^-1(x) = -(3/4)
I see that the numbers in the domain and range in one function are in the equation of the opposite function. Is there a more mathematical way of saying this? Or even a better way?
One more question:
"assume that the domain of f and f^-1 is all real numbers. Solve the equation for x using the given information."
f^-1(2x + 3) = 5 ; f(5) = 13
I'm not sure what they are asking me to do. I know I can't plug the 5 into the inverse function because then I would not be solving for x. How do I get started with this?
Thank you so much.
Jenny