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# Find the domain and range of following function?

3/√x-3

please explain

### 4 Answers

- The EnlightnerLv 49 years agoFavorite Answer
well domain is any acceptable x values. There can be no negatives under a radical and 0 cant be in the denominator so its x>3

range is the possible y values and that is going to simply be y>0

Source(s): Took AP calc in HS - Anonymous9 years ago
The domain is x > 3, xEℝ.

The smallest number that you can put into that function that doesn't result in having to square root a negative is 3. But then you would have to divide by 0 which is impossible, so the next biggest integer you can use is 4.

In short, when you have to find the domain of a function, just find the smallest number you can put into that function without getting a maths error.

----

To find the range, I put 3 into the function (3 / √(4-3) = 3√1 = 1). So the range is y ≥ 1 yEℝ. Since I can't use negative numbers that's the smallest value of y that I can get with that function.

Hope this helps!

Source(s): My maths teacher - QCLv 79 years ago
Without parentheses, we get only √x in denominator:

y = (3/√x) - 3

So domain is all values of x that do not make denominator 0 (x ≠ 0)

and all values of x that do not make value under √ negative (x ≥ 0)

Combining these results, we get: x > 0

Range:

(3/√x) > 0

(3/√x) - 3 > -3

y > -3

Domain: (0, ∞)

Range: (-3, ∞)

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Perhaps you meant y = 3/(√x - 3)

with only x under √

Denominator cannot be 0 ----> √x ≠ 3 ----> x ≠ 9

Value under √ cannot be negative -----> x ≥ 0

Domain: [0, 9) U (9, ∞)

When x is between 0 and 9, denominator < 0 and ≥ -3 ----> y ≤ -1

When x is > 9, denominator > 0 -----> y > 0

Range: (-∞, -1) U (0, ∞)

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Perhaps you meant y = 3/√(x - 3)

with all of x-3 under √

Denominator cannot be 0 ----> x - 3 ≠ 0 ----> x ≠ 3

Value under √ cannot be negative -----> x - 3 ≥ 0 ----> x ≥ 3

Combining these results, we get: x > 3

Domain: (3, ∞)

Since both numerator and denominator are both > 0, then y > 0

Range: (0, ∞)

--------------------

Next time you may want to use parentheses to avoid confusion.

Mαthmφm

- Martin FLv 69 years ago
Since denominator can't be neg solve √x-3 >/= to 0 . . .

So the domain will be all reals >/= to 9.