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)

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) (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?
------
Find the turning point (vertex).
It occurs where x = -b/(2a) = 4/(2(2)) = 1
------
Since x = 0 is to the left of x = 1 the larger
interval is (-oo,1)
------------
Cheers,
Stan H.
---------------
RELATED QUESTIONS
Functions that aren't invertible can be made invertible by restricting their domains. For (answered by greenestamps)

Can quadratic functions be invertible? For example f(x)=4x^2+12x+9 Please give the... (answered by josgarithmetic)

For each of the following functions, determine if the function is increasing, decreasing, (answered by CPhill)

For each of the following functions, determine if the function is increasing, decreasing, (answered by CPhill,ikleyn)

For each of the following functions, determine if the function is increasing, decreasing, (answered by CPhill)

Let T:R^3➜R^2 be defined as T(x, y, z) = (x+y, y-z). Is T Invertible? How can... (answered by ikleyn)

For each of the following functions, determine if the function is increasing, decreasing, (answered by CPhill)