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

  • Thread starter angela107
  • Start date
  • #1
35
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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(π‘₯)=\sqrt{x},π‘₯β‰₯0##

However, ##𝑦=𝑓(π‘₯)β‰₯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,+∞)β†’[0,+∞)##.

Is my solution correct?
 

Answers and Replies

  • #3
35,118
6,857
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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