Question

Find the domain abd range of the real function f(x)=root over 2x-1

Answer 1

answer in the picture

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