Question

find the domain and range of the function f(x)=1÷x+3_5​

Answer 1

Answer:

.

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.....

Step-by-step explanation:

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