SOLUTION: Some functions that aren't invertible can be made invertible by restricting their domains. For example, the function x^2 is invertible if we restrict x to the interval [0,infinity)

Algebra ->  Equations -> SOLUTION: Some functions that aren't invertible can be made invertible by restricting their domains. For example, the function x^2 is invertible if we restrict x to the interval [0,infinity)      Log On


   

Question 1073789: Some functions that aren't invertible can be made invertible by restricting their domains. For example, the function x^2 is invertible if we restrict x to the interval [0,infinity), or to any subset of that interval. In that case, the inverse function is square root(x). (We could also restrict x^2 to the domain (-infinity,0], in which case the inverse function would be -sqrt(x)
Similarly, by restricting the domain of the function f(x) = 2x^2-4x-5 to an interval, we can make it invertible. What is the largest such interval that includes the point x=0?Thank you.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Similarly, by restricting the domain of the function f(x) = 2x^2-4x-5 to an interval, we can make it invertible. What is the largest such interval that includes the point x=0?
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Find the turning point (vertex).
It occurs where x = -b/(2a) = 4/(2(2)) = 1
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Since x = 0 is to the left of x = 1 the larger
interval is (-oo,1)
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Cheers,
Stan H.
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