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Let f(x) = (x+2)^2-5. If the domain of f is all real numbers, then f does not have an inverse function, but if we restrict the domain of f to an interval [c,infinity), then f may have an inverse function. What is the smallest value of c we can use here, so that f does have an inverse function?

 Jul 19, 2019
 #1
avatar+792 
+3

iknow this but i cant figure this on out sorry!

😭😭

 Jul 19, 2019
 #2
avatar+105484 
+2

f(x)  = (x + 2)^2  - 5      is a parabola   with a vertex of  (-2, -5)

 

If we restict its domain  to  [ -2, infinity ),  f(x)  will be  a one-to-one function  and thus, will have an inverse

 

So...c  = -2

 

 

cool cool cool

 Jul 19, 2019

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