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(a) Let f : R -> R be defined by f(x) = x^2.  Show that f(x) has no inverse function.

(b) Let g : (0,inf) -> R be defined by g(x) = x^2.  Show that g(x) has an inverse function.

 Jun 18, 2021
 #1
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A function does not have an inverse function when 2 different x values can produce the same y value. 

f(-3) = 9

f(3) = 9

So if we were to inverse it, f(9) could be 3 or -3, making it not a function. 

Think about why g(x) has an inverese.

Can 2 different x in the domain produce the same y?

 

=^._.^=

 Jun 18, 2021

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