Question

Find domain and range of f(x) =√2x-1

Answer 1

Domain is the set of x values in which the function is defined. Range is the set of y values in which the function is defined.

Since we cannot have a negative number under the square-root

2x - 2 ≥ 0

Solve the inequality.

2x ≥ 2

x ≥ 1

The domain is [1, ∞).

To find the range, we simply plug in all the x values into the function that are within the domain. Another thing that is important to know is that as x gets closer to infinity, the value of y gets closer to certain constant but never reaches it. This y value is known as the horizontal asymptote, and serves as an indicator to how low and how high the y values can reach to.

y = √(2(1) - 2) = √0 = 0

y = √(2(2) - 2)) = √2 = 1.414

y = √(2(3) - 2) = √4 = 2

y = √(2(4) - 2) = √6 = 2.449

If we keep going, the value of y increases without any bounds. If you have a graphing calculator, you can easily confirm this.

Range is [0, ∞).

Edwin R.

A thousand thanks Michael!

Report 08/31/15

Michael W.

Edwin, just to add to Michael's answer:

Michael noted that x ≥ 1 was the domain. Yes, x can be equal to 1, because you'd be taking the square root of zero, which is totally legal. In interval notation, however, the (1, ∞) means that 1 is not included in the interval, meaning x > 1, and I don't think that's what you wanted. To show that 1 is included, you'd say [1, ∞), with a square bracket instead of a parenthesis, which says the equivalent of x ≥ 1.

Answer 2

Answer:

The domain is all real numbers greater than or equal to 0, and the range is all real numbers greater than or equal to 0

Step-by-step explanation:

The function is given to be :

f(x) = √2x - 1

Domain : It is defined as a set of all points for which the function is real and defined.

Now, The given function f(x) is a square root function and is real and defined for all the positive numbers. So, The domain of the given function f(x) is given by : 2x - 1 ≥ 0

⇒ x ≥ 1/2

Domain : All real numbers greater than or equal to 1/2

Range : It is defined as a set of all values of dependent variable for which the function is defined.

Now, To find range of the given function :

Since, square root function always writes a positive value greater than or equal to 0

So, The range consists of all the values greater than or equal to 0

⇒ Range : All real numbers greater than or equal to 0

Thus, The domain is all real numbers greater than or equal to 0, and the range is all real numbers greater than or equal to 0