Q

# Find the domain and range of the following real functions: f (x) = (9- x^2) ^1/2

Q2 (2)  Find the domain and range of the following real functions:

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

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Given function is
$f ( x ) = \sqrt { 9- x ^2 }$
Now,
Domain: These are the values of x for which f(x) is defined.
for the given f(x) we can say that, f(x) should be real and for that,9 - x2 ≥ 0 [Since a value less than 0 will give an imaginary value]
$\Rightarrow 3^2-x^2= (3-x)(3+x)\geq 0$
$\Rightarrow -3\leq x\leq 3$
Therefore,
The domain of f(x) is  $[-3,3]$
Now,
If  we put the value of x from  $[-3,3]$ we will observe that the value of function $f ( x ) = \sqrt { 9- x ^2 }$  varies from 0 to 3
Therefore,
Range of f(x) is  $[0,3]$

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