Answer:
[tex]f(x)=\left \{ {{\sqrt{1-x^2}\ \text{for $-1\le x\le 1$}} \atop {x-1\ \text{for $x>1$}}} \right.[/tex]
Step-by-step explanation:
The circle equation can be written in terms of x as ...
... y² = 1 - x²
... y = ±√(1 -x²)
The value of y will be positive when we use the positive square root. This expression is only defined for -1 ≤ x ≤ 1.
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The absolute value equation can be written as ...
... ±(y +1) = x
We're interested in the positive-going branch of this, so ...
... y + 1 = x
... y = x - 1
This will only be positive for x ≥ 1, so there is no overlap with the graph of the circle. The combined piecewise function definition will look like the expression in the answer section above.
