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. 👍 0
  2. 👎 0
  3. 👁 51

Respond to this Question

First Name

Your Response

Similar Questions

  1. Pre-caluclus

    I do not know how to solve for y to get the inverse of this question: The number of elephants in a park is estimated to be P(t)=7500 1 + 749e^(−0.15t) where t is the time in years and t = 0 corresponds to the year 1903. Find the

    asked by Anonymous on September 30, 2014
  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

    asked by Jen on October 20, 2006
  3. Inverse of log function

    Find the inverse of f(x) = log(2+x) - 4 the base is "a" Call f(x) y y = loga(2+x) -4 y+4 = loga(2+x) a^(y+4) = 2 + x x = a^(y+4) - 2 drwls, you have merely solved the equation for x. The question was to find the "inverse", so the

    asked by Jen on March 1, 2007
  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

    asked by Bob on January 11, 2016
  5. Math

    Find inverse of f if f(x)= x^2-4x+3, (for x is smaller than and equal to 2). First prove that f(x) is one to one in the defined domain of f and then obtain the inverse function. I know how to find the inverse. We just switch x and

    asked by Mahnoor on January 19, 2015
  6. Math

    I need help with these three math question. 1st question. What is the additive inverse of 5 on the 12-hour clock? 2nd question. What is the equivalent number on the 12-hour clock. -22 the choices for this question is, 5 or 2 or 3

    asked by Kimberly on February 5, 2011
  7. College Algebra

    Consider the following Matrix: A= [-2 0 1 -1 -2 1 1 -1 0 ] Choose the correct description of A. Find A−1 if it exists. Multiple Choice homework question: 1) A is Nonsingular; that is, it has an inverse. A^-1= 2) A is singular;

    asked by Moses on February 1, 2017
  8. inverse

    find f^-1 (x). (this is asking me to find the inverse) f(x) = -(x-2)^2, x If f(x)=-(x-2)^2 x

    asked by kristie on July 11, 2006
  9. Math

    y=arccos(sin(x)), find dy/dx and sketch it's graph(I guess I can do this on wolframalpha after I'm done solving the question). And by arcsin I mean inverse of the expression(written like cos^-1(sin(x)), but is not 1/cos(sinx) but

    asked by Beth on January 4, 2016
  10. MATH PLEASE HELP

    Given: Let f: X -> Y be a function. Then we have an associated function f^(-1): P(Y) -> P(X), where f^(-1) (B)⊂X is the inverse image of B⊂Y. Question: Show that f^(-1) is one-to-one if and only if f is onto. [Notes: ⊂

    asked by Nic on November 3, 2011
  11. Math: Intro to Proofs

    Given: Let f: X -> Y be a function. Then we have an associated function f^(-1): P(Y) -> P(X), where f^(-1) (B)⊂X is the inverse image of B⊂Y. Question: Show that f^(-1) is one-to-one if and only if f is onto. [Notes: ⊂

    asked by Nic on November 3, 2011

More Similar Questions