Question

If f(x)=sqrt 1\2x-10+3, which inequality can be used to find the domain of f(x)?

Answer 1

we have

$f(x)=\sqrt{\frac{x}{2}-10}+3$

we know that

The domain is determined of what's under the square root sign.

so

the term $(\frac{x}{2}-10)$ must be greater than or equal to zero

$\frac{x}{2}-10 \geq 0$

Solve for x

Adds $10$ both sides

$\frac{x}{2}-10+10 \geq 0+10$

$\frac{x}{2} \geq 10$

Multiply by $2$ both sides

$x \geq 20$

the solution is the interval---------> [20,∞)

therefore

the answer is

The inequality that can be used to find the domain of f(x) is

$\frac{x}{2}-10 \geq 0$