Question

find the domain and range of a function of f x equal to under root 9 - x square Lesson name​

Answer 1

SOLUTION :

TO DETERMINE

The domain and range of the function

$\sf{f(x) = \sqrt{9 - {x}^{2} } }$

EVALUATION

Here the given function is

$\sf{f(x) = \sqrt{9 - {x}^{2} } }$

DOMAIN :

Here f(x) is well defined when

$\sf{9 - {x}^{2} \geqslant 0\: }$

$\implies\sf{ - {x}^{2} \geqslant - 9\: }$

$\implies\sf{ {x}^{2} \leqslant 9\: }$

$\implies\sf{ - 3 \leqslant x \leqslant 3\: }$

Hence the required Domain is

$= \sf{ \{ \: x \in \mathbb{ R} \: : \: - 3 \leqslant x \leqslant 3 \: \} }$

$= \sf{ [ - 3,3 \: ] }$

RANGE :

Since for every value of x in the domain set we can get a value of f(x)

Hence the range is the set of Real numbers

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

log₁₀(10.01),Find approximate value

https://brainly.in/question/5598224