Question

Determine the domain of the following functions. Write answer in interval notation. Exercise a)

Answer 1

The domain of a square root function is all values of x that result in a radicand equal to or greater than zero.

Then, we can write and solve the following inequality:

`\begin{gathered} 10-2x\ge0 \\ \text{ Subtract 10 from both sides} \\ 10-2x-10\ge0-10 \\ -2x\ge-10 \\ \text{ Multiply by -1 from both sides of the equation (reverses the inequality)} \\ -2x\cdot-1\ge-10\cdot-1 \\ 2x\le10 \\ \text{ Divide by 2 from both sides of the equation} \\ (2x)/(2)\le(10)/(2) \\ x\le5 \end{gathered}`

This result means that the domain of the function is all values of x less than or equal to five.

Therefore, the domain of the given function in interval notation is:

`D=(-\infty,5\rbrack`