- #1

angela107

- 35

- 2

- Homework Statement
- For this question, let ##f:[0,+∞)->R## is defined by ##f(x) = √x##, 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 ##𝑓(𝑥)=\sqrt{x},𝑥≥0##

However, ##𝑦=𝑓(𝑥)≥0##, so the domain and range of ##f## are ##[0,+∞)##

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

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

Is my solution correct?

We can let ##𝑓(𝑥)=\sqrt{x},𝑥≥0##

However, ##𝑦=𝑓(𝑥)≥0##, so the domain and range of ##f## are ##[0,+∞)##

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

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

Is my solution correct?