Find the domain and range of the following real function:

(i) f(x) = –|x| 

(ii) f(x) = \( \sqrt{(9 – x^2) }\)

Asked by Abhisek | 11 months ago |  48

1 Answer

Solution :-

(i) Given,

f(x) = –|x|, x ∈ R

We know that,

As f(x) is defined for x ∈ R, the domain of f is R.

It is also seen that the range of f(x) = –|x| is all real numbers except positive real numbers.

Therefore, the range of f is given by (–∞, 0].

 

(ii) f(x) = \( \sqrt{(9 – x^2)}\)

As \( \sqrt{(9 – x^2)}\) is defined for all real numbers that are greater than or equal to –3 and less than or equal to 3, for 9 – x2 ≥ 0.

So, the domain of f(x) is {x: –3 ≤ x ≤ 3} or [–3, 3].

Now,

For any value of x in the range [–3, 3], the value of f(x) will lie between 0 and 3.

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

Answered by Pragya Singh | 11 months ago

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