Question

find the range of f(x) = ✓ x-2 / ✓3-x
please give correct answer
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Answer 1

Find the domain and range of f(x)=

(x−1)(3−x)

We have,

f(x)=

(x−1)(3−x)

Now,

Under square root the polynomial must be positive. The domain is obtained by solving:-

(x−1)(3−x)≥0

You can obtain the zeroes of the polynomial

(x−1)(3−x)=0

If

x−1=0

x=1

If

3−x=0

⇒x=3

So,

x=1,3

So the polynomial is solved in the external intervals.

x>1,x>3

So,

x∈(1,+∞)

Since the function f(x) is positive, due to result of square root,

The range includes all positive real numbers x≥0

Hence, this is the answer

Answer 2

Answer:

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Step-by-step explanation:

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