Question

I need a full answer please

Answer 1

`f(x)=\left \{ {{√(1-x^2)\ \text{for $-1\le x\le 1$}} \atop {x-1\ \text{for $x>1$}}} \right.`

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.

_____

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.