SOLUTION: For the function defined by f(x)= 2-x^2, 0 less or equal than x, use a sketch to help find a formula for f^-1(x). My answer is f^-2(x)= squrt2-x, x less or equal than 2. This I'm

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: For the function defined by f(x)= 2-x^2, 0 less or equal than x, use a sketch to help find a formula for f^-1(x). My answer is f^-2(x)= squrt2-x, x less or equal than 2. This I'm      Log On


   

Question 44663This question is from textbook Algebra and Trigonometry with Analytic geometry
: For the function defined by f(x)= 2-x^2, 0 less or equal than x, use a sketch to help find a formula for f^-1(x). My answer is f^-2(x)= squrt2-x, x less or equal than 2. This I'm not sure of. Thanks as always for looking at my post. This question is from textbook Algebra and Trigonometry with Analytic geometry

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
For the function defined by f(x)= 2-x^2, 0 less or equal than x, use a sketch to help find a formula for f^-1(x). My answer is f^-2(x)= squrt2-x, x less or equal than 2.
If you sketch f(x) you will have the right half of a parabola opening
downward with its vertex at (0,2).
The inverse is x=2-y^2
y^2=2-x
y=sqrt(2-x) with x<=2
Cheers,
Stan H.