SOLUTION: Question 3.7/9 Let f(x)=(x+1)2 Find a domain on which f is one-to-one and non-decreasing. Find the inverse of f restricted to this domain f−1(x)=

Algebra ->  Finance -> SOLUTION: Question 3.7/9 Let f(x)=(x+1)2 Find a domain on which f is one-to-one and non-decreasing. Find the inverse of f restricted to this domain f−1(x)=      Log On


   

Question 1187394: Question 3.7/9
Let f(x)=(x+1)2
Find a domain on which f is one-to-one and non-decreasing.

Find the inverse of f restricted to this domain f−1(x)=
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=%28x%2B1%29%5E2 -> a domain will be all real numbers R
Find a domain on which f+is one-to-one and non-decreasing will be restricted
0=%28x%2B1%29%5E2
x%2B1=0
x=-1
a domain on which f is one-to-one and non-decreasing is all x%3E=-1
[-1,infinity)

Find the inverse of f restricted to this domain f%5E-1%28x%29=
recall that f%28x%29=y
y=%28x%2B1%29%5E2 ......swap variables
x=%28y%2B1%29%5E2.......solve for y
y%2B1=sqrt%28x%29
y=sqrt%28x%29-1
f%5E-1%28x%29=sqrt%28x%29-1

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