Question

Find the domain of the given function.

f(x) = square root of quantity x plus three divided by quantity x plus eight times quantity x minus two.

Answer 1

Square of quantity \(x\) plus three means : \(\sqrt{x+3}\)
quantity \(x\) plus eight means : \((x+8)\)
quantity \(x\) minus two means : \((x - 2)\)
So I interpreted it as :
\[f(x) = \frac{\sqrt{x + 3}}{(x + 8)} \times (x-2)\]

Answer 2

See, in square, whatever the thing is, it cannot become Negative at any point of time.
So:
\[(x+3) \ge 0 \implies x \ge -3\]
This is first condition..

Answer 3

Second condition is, the thing in denominator cannot become \(0\)..
\[x+8 \ne 0 \implies x \ne -8\]

Answer 4

So, Domain is : All Reals greater than or equal 3..

Answer 5

*-3..

Answer 6

\[\mathbb{R} : x \ge -3\]