R=(x,y):y=√2x-1 find domain and range?

Domain: The domain of the function is all real numbers for which the expression inside the square root is non-negative. In this case, the expression inside the square root is 2x-1, so we need to find when 2x-1 is greater than or equal to 0.

2x - 1 ≥ 0
2x ≥ 1
x ≥ 1/2

Therefore, the domain of the function is all real numbers greater than or equal to 1/2.

Range: The range of the function is all real numbers that can be obtained as the output of the function for the values in the domain. Since the function is a square root function, the range will be all real numbers greater than or equal to 0.

Therefore, the range of the function is all real numbers greater than or equal to 0.

Domain:

The domain of a relation is the set of all possible input values. In this case, x is the input value, and it appears under the square root sign. Since the square root of a negative number is undefined, the input value must be greater than or equal to 1/2, so the domain is:

```
Domain = {x | x ≥ 1/2}
```

Range:

The range of a relation is the set of all possible output values. In this case, y is the output value, and it is defined as:

```
y = √2x - 1
```

Since the square root of a non-negative number is always non-negative, the output value y must be non-negative. Therefore, the range is:

```
Range = {y | y ≥ 0}
```