inverse

my question was:
find f^-1 (x). (this is asking me to find the inverse)

f(x) = -(x-2)^2, x <= 2

how do I solve this problem?>>

and you answered:
If f(x)=-(x-2)^2 x<-2, then
let y=f(x)
- y = (x-2)^2
sqrt(-y)= x-2
x(y)= sqrt (-y) + 2
g(x)= sqrt(-x) + 2
and that is the inverse function
check:
g(f(x))= sqrt( (x-2)^2) +2 =x
f(g(x)= -((sqrt(-x) + 2 -2)^2= x
since g(f(x))=f(g(x)=x, then g(x) above is the inverse. Practice these.


However, I didn't mean x<-2, but x<=2. Is this going to make a difference in the final answer?


yes, you can see that taking the root of -x means x is <=0, therefore you need to restrict the domain.
Incidentally, there's a relatively simple way to "see" what the inverse of a function looks like. If you're,respond.


could you tell me more about it?


This is a very simple device and you may or may not have seen it.
Follow the steps below
1. You need square piece of paper, but clear plastic like an overhead transparency is better. It should be square though.
2.From the lower left hand corner to the upper right hand corner, draw the diagonal. This is the line y = x, but it's also called the identity function f(x) = x.
3. Put the x and y axis through the middles of the paper so the origin is in the center.
4. Now you can draw an arbitrary function on the paper.
5. Now you flip the paper over along that diagonal.
6. Now you should be able to see the axis's and the function on the other side. Label the axis on the flipped side so that was the x axis in the neg. direction is now the pos. y axis on the flip side; the - y axis pre-flip is now + x axis post-flip.
7. The function you see through the paper post-flip is the inverse of the function pre-flip.
What you have done is reflect the function across the identity function. This is one way to view an inverse function. Try this with the function f(x) = x^2 and you will see why we only use the pos. branch of root-x. You should also see why 1-1 functions have inverses; I don't know if you've covered these.
As I said, this demo works best with clear plastic.
I should also mention that this is sometimes an exercise when you study something called the dihedral group D4; the group of rotations and reflections of a group of order 4. I don't expect you to understand this, but there is some group theory going on here too.

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. Functions - math

    The function f is such that f(x) = a^2x^2 - ax + 3b for x

  2. Functions - math

    The function f is such that f(x) = 2x + 3 for x ≥ 0. The function g is such that g(x)= ax^2 + b for x ≤ q, where a, b and q are constants. The function fg is such that fg(x)= 6x^2 − 21 for x ≤ q. i)Find the values of a

  3. Calculus (Please check my work!)

    Suppose that y = f(x) = x^2 - 4x + 4. Then on any interval where the inverse function y = f-1(x) exists, thederivative of y = f-1(x) with respect to x is: (Hint: x^2 - 4x + 4 can be factored and rewritten as "something" squared.)

  4. Algebra

    Dan works at a hardware store. The employee discount is determined by the formula d = 0.15 (c − 10 ). Use the inverse of this function to find the cost of the item for which Dan received an $18.00 discount. a. Find the inverse

  1. Precalculus

    Find the inverse of g(x)=(1/3x)-7 and then find its domain and range. I already found the inverse of the function.

  2. College Alg

    Find the inverse function of f. f(x) = 36 − x2 , 0 ≤ x ≤ 6 I can't seem to find this inverse, someone help please?

  3. math

    The cost of producing q articles is given by the function C=f(q)=100+2q. (A) Find the formula for the inverse function. (B) Explain in practical terms what the inverse function tells you. I am pretty sure the answer to A is

  4. Math- steve? reiny?

    1. Let f(x)=x^5 + 2x^3 + x - 1 Find f^-1(3) and (f^-1)'(3)? I have zero idea how to find the inverse of this function at a point 3, and how to take derivative of an inverse. 2.Let f(x)=cosx + 3x Show that f(x) is a differentiable

  1. Algebra 2

    Find the inverse of the following function: f(x) = 3x + 12 I don't think I worked this problem off correctly...I am suppose to find the inverse of the function Is this the correct way to work this problem? y= 3x + 12 x= 3y + 12 3y

  2. inverse

    If f(x)=cosx + 3 how do I find f inverse(1)? Thanks y = cos(x) + 3 the inverse of this is x = cos(y) + 3 solve for y and you have your inverse The cos function only has a range of [-1,1], so the range of f(x) is [2,4]. this means

  3. Algebra

    Let p(x)=2x^3-113 and let q be the inverse of p. Find q(137). Please explain in steps. I posted this already but I did not list my steps. The first step would be to find the inverse of 2x^3-113 which would be: y=(x+113/2)^1/3. and

  4. Algebra

    Consider the following matrix. A = 7, -5 -4, 3 Choose the correct description of A Find A^−1 if it exists. Answer either Choice 1, or Choice 2: CHOICE 1: A is nonsingular; that is, it has an inverse. A^-1 = _________ or CHOICE 2

You can view more similar questions or ask a new question.