# How do you find the domain and range of f(x) = -2 * sqrt(x-3) + 1?

Jun 20, 2017

Domain: $x \ge 3$ In interval notation : $\left[3 , \infty\right)$
Range: $f \left(x\right) \le 1$. In interval notation : $\left(- \infty , 1\right]$

#### Explanation:

$f \left(x\right) = - 2 \cdot \sqrt{x - 3} + 1$

Domain: Under root should be $\ge 0 \therefore x - 3 \ge 0 \mathmr{and} x \ge 3$

Domain: $x \ge 3$ In interval notation : $\left[3 , \infty\right)$

Range: When x=3 ; f(x)= 1. For x>3 ; f(x) goes on decreasing.

Range: $f \left(x\right) \le 1$. In interval notation : $\left(- \infty , 1\right]$

graph{-2*(x-3)^0.5+1 [-10, 10, -5, 5]} [Ans]