Question

Find the domain and range of the real function f(x)=√9-x^2

Answer 1

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Here we have,

f(x) = √9 - x²

Here,

f(x) is not defined when the value of (9 - x²)<0

As,

f(x) is defined when the value of (9 - x²)≥0

So,

(9 - x²) ≥ 0

x² - 9 ≤ 0

x² ≥ -3

-3 ≤ x ≤ 3

x € [-3 , 3]

Therefore,

dom (f) = [-3 , 3]

Here,

For each

x € [-3 , 3]

f(x) = √9 - x² have value in interval [0,3].

Therefore,

Range (f) = [0,3]

So,

dom (f) = [-3 , 3] also range (f) = [0 , 3]