Let f ( x ) = ( x + 9 )^2

Question

Give the largest domain on which  is one-to-one and non-decreasing.  _____

Give the range of 

Find the inverse of restricted to the domain above.

 _____

Give the domain of f^−1(x)= _____

Give the range of f^−1(x)= _____

 .  

Answer 1

The graph of f(x) = (x+9)² is a parabola opening upward with lowest point (-9,0).

The function is 1-1 and non-decreasing on the interval [-9, ∞) The range is [0, ∞)

To find the inverse function, let y = f(x), switch x and y and then solve for y. We get y = f^-1(x) = √x - 9 The domain of f^-1(x) is the range of the restricted f(x) and the range of f^-1(x) is the domain of the restricted f(x).

So, domain f^-1 is [0,∞) and range f^-1 is [-9, ∞).