# How do you find the domain and range of f(x)= sqrt(6x-10)?

Aug 28, 2017

Domain : $x \ge \frac{5}{3} \mathmr{and} \left[\frac{5}{3} , \infty\right)$. Range: $f \left(x\right) \ge 0 \mathmr{and} \left[0 , \infty\right)$

#### Explanation:

$f \left(x\right) = \sqrt{6 x - 10}$ . Domain: Under root should $\ge 0$

$6 x - 10 \ge 0 \mathmr{and} 6 x \ge 10 \mathmr{and} x \ge \frac{10}{6} \mathmr{and} x \ge \frac{5}{3} \therefore$ Domain is

$x \ge \frac{5}{3} \mathmr{and} \left[\frac{5}{3} , \infty\right)$

Range: f(x) is not a negative number, i.e $f \left(x\right) \ge 0 \mathmr{and} \left[0 , \infty\right)$

Domain is $x \ge \frac{5}{3} \mathmr{and} \left[\frac{5}{3} , \infty\right)$ and Range is $f \left(x\right) \ge 0 \mathmr{and} \left[0 , \infty\right)$

graph{(6x-10)^0.5 [-10, 10, -5, 5]} [Ans]