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# Inverse Functions

+1
715
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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?

Apr 4, 2019
edited by MemeLord  Apr 4, 2019
edited by MemeLord  Apr 4, 2019

#3
+118471
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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    $$[-\pi/2,\pi/2]$$

Apr 4, 2019