Question 1157185: Find the inverse of the function
(a) f(x)= x^2+2x-1, x>0
Found 3 solutions by josgarithmetic, MathLover1, Edwin McCravy:
Answer by josgarithmetic(39625)   (Show Source):
Answer by MathLover1(20850)  (Show Source):
Answer by Edwin McCravy(20060)  (Show Source):
You can put this solution on YOUR website!
The above two solutions are incorrect.
Find the inverse of the function
f(x)= x^2+2x-1, x>0That's this parabola with the dotted part discarded.
We want to find its inverse:
So f(x) is this graph:
We want to find the equation of its inverse, the blue graph below,
which is the projection of f(x) across the "identity line", which is
the green dotted line below through the origin that leans right at
am angle of 45°, and that has equation y=x.
To find the equation for the graph of the blue curve,
 
Step 1. Change f(x) to y
Step 2. Interchange x and y
 
Step 3. Solve for y
Swap sides:
Use quadratic formula with a=1, b=2, c=-1-x
We must require that y > 0, and therefore
This tells us that we can only use the + sign:
Square both sides:
So equation of the blue curve is
Step 4. Finally, change y to f-1(x)
Edwin
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