SOLUTION: Does the function f(x)=x^2 have an inverse function? Explain why or why not and illustrate with a sketch of the inverse

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Question 892311: Does the function f(x)=x^2 have an inverse function? Explain why or why not and illustrate with a sketch of the inverse
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
It has an inverse however it is not a function.
If you interchange x and y and solve for the new y (the inverse), you get,
x=y%5E2
y=0+%2B-+sqrt%28x%29
Since you have the plus/minus in front of the sqrt%28x%29, you have two y values for every x value, which violates the definition of a function.
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The original function
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E2%29
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The original function and its inverse
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E2%2Csqrt%28x%29%2C-sqrt%28x%29%29