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Suppose g(x)=4x^2+8x+13. Does g have an inverse? If so, find g^{-1}(25). If not, enter "undef".

 Oct 29, 2020
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Suppose g(x)=4x^2+8x+13. Does g have an inverse? If so, find g^{-1}(25). If not, enter "undef".

 

g(x) only has an inverse if you restrict the domain.

 

g(x) is a concave up parabola.  At the vertex       \(x= \frac{-b}{2a}=\frac{-8}{8}=-1\)

 

So if you restrict the domain to x>-1   or   X<-1     then it will have an inverse, otherwise, it does not.

 

Since no restriction is given, the inverse is undefined.

 

https://www.geogebra.org/classic/p9zznufj

 

 Oct 29, 2020

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