Question

Find the domain of f and write your answer in interval notation. f(x) = 9/10 + 4x + 6

Answer 1

The domain of a function is the set of all posible values that its input can take.

To find it, we should analyze the rule of correspondence of the function to see if it includes restrictions over the variable that works as input. In this case, we can see that x appears inside a square root. The expression inside the square root must be greater or equal to 0. Then:

`\begin{gathered} 10+4x\ge0 \\ \Rightarrow4x\ge-10 \\ \Rightarrow x\ge-(10)/(4) \\ \Rightarrow x\ge-(5)/(2) \end{gathered}`

The domain of f is the set of all real numbers x such that:

`-(5)/(2)\le x`

In interval notation:

`x\in\lbrack-(5)/(2),\infty)`

Therefore, the domain of the function is:

`\lbrack-(5)/(2),\infty)`