Question

given the function $g(x) = \sqrt3{-2x} + 2$, identify the x-intercept (1 point) the x-intercept is (\boxed{ },0)

Explanation:

Step1: Recall x-intercept definition

The x - intercept of a function \(y = g(x)\) is the value of \(x\) when \(y = 0\), i.e., we set \(g(x)=0\) and solve for \(x\).
Given \(g(x)=\sqrt[3]{- 2x}+2\), set \(g(x) = 0\):

$$0=\sqrt[3]{-2x}+2$$

Step2: Isolate the cube - root term

Subtract 2 from both sides of the equation:

$$\sqrt[3]{-2x}=- 2$$

Step3: Eliminate the cube - root

Cube both sides of the equation. Recall that \((\sqrt[3]{a})^3=a\). So, cubing both sides of \(\sqrt[3]{-2x}=-2\) gives:

$$(\sqrt[3]{-2x})^3=(-2)^3$$

$$ - 2x=-8$$

Step4: Solve for x

Divide both sides of the equation \(-2x = - 8\) by \(-2\):

$$x=\frac{-8}{-2}=4$$

Answer:

The x - intercept is \((4,0)\)