How do you find the domain and range of $f (x) = \sqrt{x - 2}$ $f(x) =sqrt(x-2)$ ?

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Answer 1 · 2018-03-11T06:46:03

Domain $\in [2, \infty)$ $in [2,oo)$

Range $\in [0, \infty)$ $in [0,oo)$

graph{sqrt(x-2 [-10, 10, -5, 5]}

Simply draw out the function.

The standard root function is:

$y = a \cdot \sqrt{(x - h)} + k$ $y=a*sqrt((x-h)) +k$

where $x - h \geq 0$ $x-h>=0$

In a square root function, the number inside the root sign CANNOT be $< 0$ $<0$

∴ $x - 2 \geq 0$ $x-2>=0$

∴ $x \geq 2$ $x>=2$

∴ Domain $\in [2, \infty)$ $in [2,oo)$

As for range, there is no K value in the function we were given
∴ the range begins at 0 to infinity.

Range $\in [0, \infty)$ $in [0,oo)$

How do you find the domain and range of f(x) =sqrt(x-2)f(x)=√x−2f(x) =sqrt(x-2)?