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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'.

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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".

waffles  Oct 25, 2017
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#1
+78604
+2

Not a strict inverse, since it's not one-to-one

However.....it we restict the domain to [-1, inf )   we have

y = 4x^2 + 8x + 13

y - 13 + 4  =  4[ x^2 + 2x + 1]

y - 9  =  4 ( x + 1)^2

[ y - 9] / 4   =  (x + 1)^2

√ [ (y - 9) / 4 ]  =  x + 1

√ [ (y - 9) / 4 ]  - 1  = x     swap x and y    and for y write f-1 (x)

√ [ (x - 9) / 4 ]  - 1  = y  =  f-1 (x)

So  f-1 (25 )    =   √ [ (25 - 9) / 4 ]  - 1  =  √ [ 16 / 4 ]  - 1   = √4 - 1  = 2 - 1 =   1

CPhill  Oct 25, 2017
#2
+355
0

I think that's incorrect

waffles  Oct 25, 2017
#3
+78604
+1

Then I suppose the domain is not allowed to be restricted.....so....there is no inverse in this case

CPhill  Oct 25, 2017

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