Question

Determine the domain of f(x)=√4x-3 in set builder notation

Answer 1

To determine the domain of this function, we have to remember that there are not real square roots for negative values, it means

`4x-3\ge0`

Solve for x in the inequality

`\begin{gathered} 4x-3\ge0 \\ 4x\ge3 \\ x\ge(3)/(4) \\ \end{gathered}`

x is more than or equal 3/4

In set builder notation it is written this way

`D=\lbrace x\in R\text{ l }x\ge(3)/(4)\rbrace`