SOLUTION: For what domain are f(x) = x^2 and g(x)=√x inverse functions? Make sure you use set builder notation.
Explain how you can tell that f(x) = x^3 and g(x)= ∛x are inve
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-> SOLUTION: For what domain are f(x) = x^2 and g(x)=√x inverse functions? Make sure you use set builder notation.
Explain how you can tell that f(x) = x^3 and g(x)= ∛x are inve
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Question 1105777: For what domain are f(x) = x^2 and g(x)=√x inverse functions? Make sure you use set builder notation.
Explain how you can tell that f(x) = x^3 and g(x)= ∛x are inverse functions.
Example of two more functions that are inverses of each other.
List a function besides f(x) = -x, f(x) = x, f(x) = 1/x, or f(x)=-1/x that is its own inverse. Answer by greenestamps(13203) (Show Source):
For the parts of your question about other pairs of functions that are inverses of each other, or are their own inverses, see answer 720669 to question 1105780 on this site.
For the other questions....
You can find the domain on which y=x^2 and y=sqrt(x) are inverses by graphing the two functions and seeing for what values of x the two graphs have symmetry with respect to the line y=x. Here is a graph; y=x^2 red, y=sqrt(x) green, y=x (blue):
You can see that y=sqrt(x) is the inverse of y=x^2 on the domain [0,infinity).
To show that y=x^3 and y=cube root of x are inverses, you can simply demonstrate the fact algebraically. Or you could graph the two functions (red; green) and observe that they are symmetrical with respect to the line y=x (blue):
Hmmmm.... Interesting -- the graphing software on this site is not able to draw the negative branch of y=cube root of x....
