- #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?