What is the domain of the function?

Question

1.) √2x-3 
2.) 4x+3/x-5 
3. 2/x^2-4x 
4.) 3x^2+1

Answer 1

(1).

The expression is √(2x - 3).

Let the function f(x) = √(2x - 3).

The domain of a function is all values of x, those makes the function mathematically correct.

Since there shouldn't be any negative numbers in the square root.

The expression (2x - 3) should be zero or positive.

2x - 3 ≥ 0

2x ≥ 3

x ≥ 3/2.

The domain of the above function is [3/2, ∞).

Answer 2

(2).

The expression is (4x + 3)/(x - 5).

Let the function f(x) = (4x + 3)/(x - 5).

The domain of a function is all values of x, those makes the function mathematically correct.

Since there shouldn't be denominator zero.

Denominator = x - 5 ≠ 0.

x ≠ 5

The domain of the above function is (- ∞, ∞) - 5.

 

Answer 3

(3).

The expression is 2/(x² - 4x).

Let the function f(x) = 2/(x² - 4x).

The domain of a function is all values of x, those makes the function mathematically correct.

Since there shouldn't be denominator zero.

Denominator = x² - 4x ≠ 0.

x(x - 4) ≠ 0

x ≠ 0 and x - 4 ≠ 0

x ≠ 0 and x ≠ 4

The domain of the above function is (- ∞, ∞) - {0, 4}.

 

Answer 4

(4).

The expression is 3x² + 1.

Let the function f(x) = 3x² + 1.

The function f(x) = 3x² + 1 is a quadratic function or parabola function. There are no rational or radical expressions, so there is nothing that will restrict the domain. Any real number can be used for x to get a meaningful output.

The domain of the above function is (- ∞, ∞).