+0  
 
0
373
3
avatar+644 

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
 #1
avatar+92808 
+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

 

 

cool cool cool

CPhill  Oct 25, 2017
 #2
avatar+644 
0

I think that's incorrect

waffles  Oct 25, 2017
 #3
avatar+92808 
+1

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

 

 

cool cool cool

CPhill  Oct 25, 2017

7 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.