Question 72950: I need some serious help. I need to know how to solve some equations. I have a test coming up and I am STUCK!
For the function defined by f(x) =2-x^2, 0 (greater than,or equalto) x, use a sketch to help find formula for f-1(x).
Someone please show me how to do this.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! For the function defined by f(x) =2-x^2, 0 (greater than,or equalto) x, use a sketch to help find formula for f-1(x).
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Your f(x) is the right half of a parabola with vertex at (0,2) and opening
downward.
Draw the line y=x on the same coordinate axes.
Now, "reflect" the curve in the line y=x.
Each point (a,b) in the original curve will become (b,a) in the new curve.
(0,2) has as its reflection the point (2,0).
Do this for all the points of the curve to get a sketch of f^-1(x), which
is the inverse of f(x)
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This is the graph of f(x); I can't show you f^-1(x).
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Cheers,
Stan H.
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