Question

Find the domain and range of the following real function:

f(x) = `sqrt(9 - x^2)`

Answer 1

f(x) = `sqrt(9 - x^2)`

Since `sqrt(9 - x^2)` is defined for all real numbers that are greater than or equal to –3 and less than or equal to 3, the domain of f(x) is {x : –3 ≤ x ≤ 3} or [–3, 3].

For any value of x such that –3 ≤ x ≤ 3, the value of f(x) will lie between 0 and 3.

∴The range of f(x) is {x: 0 ≤ x ≤ 3} or [0, 3].