Determining the domain and range for the function ##f^{-1}##

  • #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?
 
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  • #2
Hi. It seems all right.
 
  • #3
The work is correct. The domain and range for this function are the same -- ##[0, \infty)##, so the domain and range for its inverse are also the same sets.
 

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