- #1

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- Homework Statement:
- For this question, let ##f:[0,+β)->R## is defined by ##f(x) = βx##, and let ##f^{-1}(x)## be its inverse function. What is the domain and range of the function ##f^{-1}(x)##?

- Relevant Equations:
- n/a

The domain and range of this function will be the same.

We can let ##π(π₯)=\sqrt{x},π₯β₯0##

However, ##π¦=π(π₯)β₯0##, so the domain and range of ##f## are ##[0,+β)##

And since ##f## is a function, ##f^{-1}s## domain is the range of ##f## and ##f^{-1}s## range is ##fβs## domain.

In other words, the domain and range of ##f^{-1}:[0,+β)β[0,+β)##.

Is my solution correct?

We can let ##π(π₯)=\sqrt{x},π₯β₯0##

However, ##π¦=π(π₯)β₯0##, so the domain and range of ##f## are ##[0,+β)##

And since ##f## is a function, ##f^{-1}s## domain is the range of ##f## and ##f^{-1}s## range is ##fβs## domain.

In other words, the domain and range of ##f^{-1}:[0,+β)β[0,+β)##.

Is my solution correct?