Question

Determinați domeniul de definiție al funcției f:D→R, f(x)=(√2-3x)+2

Answer 1

The domain is all real numbers less than or equal to two-third

Explanation:

The question in English is

Determine the domain of the function f :D→R,
`f(x)=√(2-3x)+2`

we know that

The radicand of the function must be greater than or equal to zero

so

`2-3x \geq 0`

Solve the inequality for x

subtract 2 both sides

`-3x \geq -2`

Multiply by -1 both sides

`3x \leq 2`

Divide by 3 both sides

`x \leq (2)/(3)`

The solution is the interval ----> (-∞,2/3]

therefore

The domain is all real numbers less than or equal to two-third