- #1
What are Direct and Inverse Images in Mathematics?
- Thread starter phillyolly
- Start date
-
- Tags
- Images
- #2
Raskolnikov
- 193
- 2
You did part (a) correctly!
Part (b):
If h = g \circ f, then h^{-1} = f^{-1} \circ g^{-1}.
Look at the boundaries of G. They will give you the boundaries of its inverse image. This isn't ALWAYS the case, but our function here is pretty simple so it will work out well.
Part (b):
If h = g \circ f, then h^{-1} = f^{-1} \circ g^{-1}.
Look at the boundaries of G. They will give you the boundaries of its inverse image. This isn't ALWAYS the case, but our function here is pretty simple so it will work out well.
- #3
- #4
Raskolnikov
- 193
- 2
mhmm! and a nice self-assuring way to check that you "almost definitely" got it right is the fact that f(\{x : -2 \le x \le 0\}) = G. I say "almost definitely" because it could happen that you luck out and it works even though your answer's wrong...but let's not worry about that haha. you got it right!
- #5
phillyolly
- 157
- 0
It turns out, I am not too dumb, yay! (Thank you for your patience, Raskolnikov.)
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Hello,
This is the attachment, the steps to solution are pretty clear. I guess there is a mistake on the highlighted part that prompts this thread.
Ought to be ##3^{n+1} (n+2)-6## and not ##3^n(n+2)-6##. Unless i missed something, on another note, i find the first method (induction) better than second one (method of differences).
Similar threads
Hot Threads
-
Prove that the integral is equal to ##\pi^2/8##
- Started by Meden Agan
- Replies: 96
- Calculus and Beyond Homework Help
-
Solving the wave equation with piecewise initial conditions
- Started by songoku
- Replies: 11
- Calculus and Beyond Homework Help
-
Area of loop in x-y plane
- Started by littlemathquark
- Replies: 20
- Calculus and Beyond Homework Help
-
Solve this problem that involves induction
- Started by chwala
- Replies: 7
- Calculus and Beyond Homework Help
Recent Insights
-
Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect
- Started by Greg Bernhardt
- Replies: 7
- Quantum Physics
-
Insights What Exactly is Dirac’s Delta Function? - Insight
- Started by Greg Bernhardt
- Replies: 0
- General Math
-
Insights Relativator (Circular Slide-Rule): Simulated with Desmos - Insight
- Started by Greg Bernhardt
- Replies: 0
- Special and General Relativity
-
Insights Fixing Things Which Can Go Wrong With Complex Numbers
- Started by PAllen
- Replies: 7
- General Math
-
Insights Fermat's Last Theorem
- Started by fresh_42
- Replies: 78
- General Math
-
Insights Why Vector Spaces Explain The World: A Historical Perspective
- Started by fresh_42
- Replies: 0
- General Math