+81 Don't the domain and range of a function just swap for the inverse function?
Example-
F(x)-
Domain: [9, \(\infty\))
Range: (\(-\infty\),\(\infty\))
F-1(x)-
Domain: (\(-\infty\),\(\infty\))
Range: [9, \(\infty\))
Is that correct?
+118690 Not quite,
The range is often more limited for the inverse.
Further constrainst on range often have to be introduced because the inverse must also be a function
Each x value must have AT MOST one y value.
eg
\(f(x)=sin x\) domain is all real x and range is [-1,1]
\(f^{-1}(x)=sin^{-1}x\) domain is [-1,1] but range must be limited. Uusally it is limited to \([-\pi/2,\pi/2]\)
