Question

find domain of f(x)=root(x-2) + root(x-3)

Answer 1

$f(x) = \sqrt{x - 2} + \sqrt{x - 3}$

Since the number under the root must be greater than or equal to zero:

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$x - 2 \geqslant 0 \\ \\ x \geqslant 2$

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$x - 3 \geqslant 0 \\ \\ x \geqslant 3$

Combining both, we get $x \geqslant 3$

Thus domain of the function f(x) is [3, infinity)

Answer 2

$f(x) = \sqrt{x - 2} + \sqrt{x - 3}$
The number inside the root cannot be negative. So it should be zero or greater than zero.

$x - 2 \geqslant 0 \\ x \geqslant 2$

and

$x - 3 \geqslant 0 \\ x \geqslant 3$
from both the value of x be concluded that
$x \geqslant 3$
$domain = [3, \infty )$