Question

y=√4x-13 find the domain

can somebody explain step by step please

Answer 1

how far does the square root extend?

is it \(\Large y = \sqrt{4x-13}\) ??

OR is it \(\Large y = \sqrt{4x}-13\) ??

Answer 2

the first one

Answer 3

You cannot have the terms under the square root be negative, so we have to force 4x-13 to be 0 or positive

which means you need to solve this for x

\[\Large 4x - 13 \ge 0\]

Answer 4

what do you get when you do so?

Answer 5

\[4x \ge 13\]

Answer 6

you can then divide both sides by 4 to get

\[\Large x \ge \frac{13}{4}\]

Answer 7

so the domain is the set of all real numbers x such that \(\Large x \ge \frac{13}{4}\)