Question

Find the inverse of f(x) = x^2 + 2x for x \(\le\) -1 and g(x) = x^2 + 2x for x \(\ge\) -1. State the domain and range for the inverse functions. For f(x), domain is [-∞ , -1], what about the range?

Answer 1

first you can think (x+1)^2-1=y then get "x" alone and change the"x" with "y" to get the inverse function

Answer 2

Thanks! But I know how to find the inverse, I just don't know how to find the corresponding domain and range :(

Answer 3

the inverse function appears as f(x)'=sqrt(x+1)-1 and for is less than -1 the sqrt becomes negative and the domain has no value but i guess :) only the value -1 makes sense for x is less than or equal to -1

Answer 4

Would you mind telling me what you get for the range of f(x) first?

Answer 5

(I'm not looking for direct answer but I have to know how it works, so that I can work out the domain and range for the inverse function. FYI, it's not homework/quiz/exam question. Just a problem I have when I'm doing my revision)

Answer 6

Range of f(x) is all the values, f(x) can take.Is there any value your f(x) can't take ??
Also remember this:
Range of f(x) = Domain of inverse of f(x)
Domain of f(x) = Range of inverse of f(x).
Does this help??

Answer 7

For f(x), actually, there is a condition, i.e. f(x) = x^2 + 2x for x \(\in\) (-\(\infty\) , -1].
For the range.. I'm really not sure of that. Since I don't know if x^2 + 2x > 0 or not,
Is the range of f(x) = [-1, + \(\infty\))?

Answer 8

yup.

Answer 9

So, domain of f\(^{-1}\)(x) = [-1, + ∞) and range f\(^{-1}\)(x) = (-∞, -1] ?