Give an example of another function whose inverse is only defined if we restrict the domain of the original function.
(in general, a function must be one-to-one in order to have an inverse function. some functions, though, have inverses that are very useful but require us to restrict the original function to an interval where it is one-to-one. this is the case with all of our trigonometric functions.)

  f(x) = x^2

Step-by-step explanation:

The square root function is defined to have a non-negative range only. That corresponds to restricting the domain of f(x) = x^2 to positive values of x.

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The attached graph shows the domain-restricted f(x)=x² in solid red and the corresponding f⁻¹(x) = √x in solid blue. The other halves of those curves are shown as dotted lines (and are inverse functions of each other, too). The dashed orange line is the line of reflection between a function and its inverse.

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.

i need more details

step-by-step explanation: