SOLUTION: Given the function, f(x)=(x+2)^2, which is not one-to-one, a) Restrict the function's domain so that the resulting function is one-one. b)Find the inverse of the function with

Algebra ->  Graphs -> SOLUTION: Given the function, f(x)=(x+2)^2, which is not one-to-one, a) Restrict the function's domain so that the resulting function is one-one. b)Find the inverse of the function with      Log On


   

Question 803358: Given the function, f(x)=(x+2)^2, which is not one-to-one,
a) Restrict the function's domain so that the resulting function is one-one.
b)Find the inverse of the function with the restricted domain.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Pick either the left side or the right side of the vertex. This point is at (-2,0), so I will pick the left side of f%28x%29=%28x%2B2%29%5E2, for x%3C=-2. This will be one-to-one.

The cheap way to get its inverse is x=%28y%2B2%29%5E2,
y%2B2=0%2B-+sqrt%28x%29%7D%7D%0D%0A%7B%7B%7By=-2%2B-+sqrt%28x%29, obtained from the one-to-one function for x<=-2

between y=-2-sqrt%28x%29 and y=-2%2Bsqrt%28x%29, you want the one that is decreaing; looking at a graph would help... It would be highlight%28y=-2-sqrt%28x%29%29

graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28x%2B2%29%5E2%2C-2-sqrt%28x%29%29