Question

Find the domain and range of the function. (Enter your answers using interval notation.) h(x) = √4 − x^2

Answer 1

Answer:

The range and domain of this function is [-2, 2]

Step-by-step explanation:

For the domain it must be fulfilled that $(4-x^2)\geq 0$. Then, $(2 + x) (2-x)\geq 0$. This expression is true for the values of $x$ that make the factors simultaneously non-negative or non-positive.

Case non-negative factors

$2 + x \geq 0$ implies that $x \geq -2$, that is $[-2, +\infty]$

$2-x \geq 0$ implies that $x \leq 2$, that is, $(-\infty, 2]$. The intersection of the previous sets is [-2, 2].

Case non positive factors

$2 + x \leq 0$ implies that $x \leq -2$, that is $(-\infty, -2]$

$2-x \leq 0$ implies that $2 \leq x$, that is, $[2,+\infty)$. The intersection of the previous sets is empty.

Then the domain of the function is [-2, 2]

The range of this function is the domain of its inverse. The inverse of the function is itself, so the range is [-2, 2]