Question

Which of the following describes the domain of the piecewise function

Answer 1

(c) (-∞, -2) ∪ (-2, 1) ∪ (1, ∞)

Explanation:

You want the domain of the given piecewise-defined function.

x < 2

For x < 2, the function is ...

`g(x)=(x^2+2x)/(x^2+x-2)-(x(x+2))/((x-1)(x+2))=(x)/(x-1)\quad x\\e\{-2,1\}`

Both of these exclusions are in the region x < 2, so both must be excluded from the domain.

x ≥ 2

The log function is defined for all values x > -2, so there are no exclusions in this region.

The domain is (-∞, -2) ∪ (-2, 1) ∪ (1, ∞).