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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 $[0,\infty)$, or to any subset of that interval. In that case, the inverse function is $\sqrt{x}$. (We could also restrict $x^2$ to the domain $(-\infty,0]$, in which case the inverse function would be $-\sqrt{x}$.)

 

Similarly, by restricting the domain of the function $f(x) = 10x - 4$ to an interval, we can make it invertible. What is the largest such interval that includes the point $x = 0$?  (In this case, "the largest such interval" refers to the interval that contains all other such intervals.)

 
 Feb 18, 2025

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