Question

Identify and explain any restrictions on the variable x in the expression `sqrt(4x-2)`?

Answer 1

See explanation below

Explanation:

Square root is an expresion defined only for postive real numbers. Do not have sense expresions like `sqrt(-1)` because there is no any number `x` such that `x^2=-1`. This type of expresions have solution in a bigger set of numbers called Complex.

In our case `sqrt(4x-2)` we have to be sures that `4x-2` is positive or zero. Then we express this fact by

`4x-2>=0` it's say
`4x>=2`
`x>=2/4`
`x>=1/2`

Thus, our expresion only have sense in `RR` if we choose x bigger or equal to `1/2`

The restriction is `x>=1/2`, or expressed in interval form `[1/2,oo)`