Question

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

Answer 1

Answer:

Domain and range...

Step-by-step explanation:

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

Note that if x² has a value greater than 9, then the value of f(x) will not be real.

So,

${x}^{2} \leqslant 9 \\ \\ - 3 \leqslant x \leqslant 3$

So, the domain of f (x) is [-3, 3].

Ans talking about the range,

What is the smallest possible value for x²?

That is 0.

So, if x = 0, then x² = 0.

Or, f (x) = (+ or -) 3

So, the range of the function is [-3, 3]

• Feeling something wrong with 0?

Yes, 0 is a special point of this function. Such a point is called point of discontinuity ( this is also the point of INFLEXION).

And here is a notice (and request) for you, My friend...

If you have more interesting mathematical problems, then please mail me at:-

[email protected]

I'm a 10th graded student and I love learning mathematics. So I keep learning new topics. So please email me your problems.

This will be helpful for both of us.

And don't be worried about the standard of the problem. Even if I'm a 10th graded student, I would solve ANYTHING.

Just share.