SOLUTION: Question 3.7/12 Let f(x)=(x+1)2 Give the largest domain on which f is one-to-one and non-decreasing= Give the range of f= Find the inverse of f restricted to the domain ab

Question 1187396: Question 3.7/12
Let f(x)=(x+1)2
Give the largest domain on which f is one-to-one and non-decreasing=
Give the range of f=
Find the inverse of f restricted to the domain above f-1(x)=
Give the domain of f-1 =
Give the range of f-1=
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The function is a quadratic function, meaning a polynomial function of degree 2.
Those functions have graphs like this or the same curve upside down.
They are symmetrical with a vertex that is a maximum or minimum, separating a decreasing branch from an increasing branch.
You realize that for , and , but for any other number .
The graph decreases from any value of , and increases for .
The largest domain on which f is one-to-one and non-decreasing is [-1,infinity), or .
The range is [0,infinity), because , and for it increases without bounds.
To find the inverse we swap and in the function defined as only when <--> , and solve for
we get for , whose solution is <--> .
The inverse function is for .

has domain [0,infinity) or and range [-1,infinity) or
The domain of an inverse function is the range of the domain-restricted function, and the range of the inverse is the restricted dominion.
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