# How do you find domain and range for  f(x) = sqrt(7x + 2)?

Jun 28, 2018

The domain is $x \in \left[- \frac{2}{7} , + \infty\right)$. The range is $y \in \left[0 , + \infty\right)$

#### Explanation:

Let $y = \sqrt{7 x + 2}$

What's under the square root sign is $\ge 0$

Therefore,

$7 x + 2 \ge 0$

$\implies$, $x \ge - \frac{2}{7}$

The domain is $x \in \left[- \frac{2}{7} , + \infty\right)$

When,

$x = - \frac{2}{7}$, $\implies$, $y = 0$

And

${\lim}_{x \to + \infty} \sqrt{7 x + 2} = + \infty$

Therefore,

The range is $y \in \left[0 , + \infty\right)$

graph{sqrt(7x+2) [-7.06, 21.42, -7.46, 6.78]}