SOLUTION: 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 $[0,\infty)$,
Algebra ->
Functions
-> SOLUTION: 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 $[0,\infty)$,
Log On
Question 1209620: 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.) Answer by greenestamps(13208) (Show Source):
