Problem 9. Define f, g: I→ R² by f(x) = (x,0), g(x) = (0,r). a. Give an explicit expression for a homotopy from f to g. for a homotopy from g to f. b. Give an explicit expression

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**Problem 9**: Define \( f, g : I \to \mathbb{R}^2 \) by 

\[ f(x) = (x,0), \quad g(x) = (0, x). \]

a. Give an explicit expression for a homotopy from \( f \) to \( g \).

b. Give an explicit expression for a homotopy from \( g \) to \( f \).

---

This text is from a mathematical assignment or exercise related to the concept of homotopy in topology. There are no graphs or diagrams in the image.
Transcribed Image Text:Certainly! Here is the transcription of the provided text: --- **Problem 9**: Define \( f, g : I \to \mathbb{R}^2 \) by \[ f(x) = (x,0), \quad g(x) = (0, x). \] a. Give an explicit expression for a homotopy from \( f \) to \( g \). b. Give an explicit expression for a homotopy from \( g \) to \( f \). --- This text is from a mathematical assignment or exercise related to the concept of homotopy in topology. There are no graphs or diagrams in the image.
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