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The interval [a,b] $\subset$ $\mathbb{R}$ and interval [0,1] $\subset$ $\mathbb{R}$ are homeomorphic in their standard topologies. [closed]

Problem: The interval $[a,b]$ $\subset$ $\mathbb{R}$ and interval $[0,1]$ $\subset$ $\mathbb{R}$ are homeomorphic in their standard topologies. Definition of Homeomorphism: We call the underlying bijection of a topological equivalence $h : X \to Y$ a homeomorphism. We say X and Y are homeomorphic. This is how I showed it. Let us define a function $f:[a,b]$$\to$$[0,1]$ […]