Q. 5 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 47– 62, find the domain of each function. 

$h\left(x\right)=\sqrt{3x - 12}$

Step-by-Step Solution

Answer

The domain of the given function is $\left\{x\right|x\ge 4\}$

Step 1. Given Information

In the given problems we have to find the domain of given function.

$h\left(x\right)=\sqrt{3x - 12}$

Step 2. The function h tells us to take the square root of 3 x - 12 .

But only non-negative numbers have real square roots, so the expression under the square root (the radicand) must be non-negative (greater than or equal to zero).

Step 3. This requires that

$3x-12\ge 0$

Add 12 on both side

$$\begin{gathered} 3x-12+12\ge 0+12 \\ 3x\ge 12 \end{gathered}$$

Divide by 3 on both side

$\frac{3}{3}x\ge \frac{12}{3}$

$x\ge 4$

Step 4. The domain of h is

$\left\{x\right|x\ge 4\}$